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In [[algebraic geometry]], the '''Mumford–Tate group''' (or '''Hodge group''') ''MT''(''F'') constructed from a [[Hodge structure]] ''F'' is a certain [[algebraic group]] ''G''. When ''F'' is given by a [[rational representation]] of an [[algebraic torus]], the definition of ''G'' is as the [[Zariski closure]] of the image in the representation of the [[circle group]], over the [[rational numbers]]. {{harvs|txt|authorlink=David Mumford|last=Mumford|year=1966}} introduced Mumford–Tate groups over the complex numbers under the name of Hodge groups. {{harvtxt|Serre|1967}} introduced the ''p''-adic analogue of Mumford's construction for [[Hodge–Tate module]]s, using the work of {{harvs|txt|last=Tate|authorlink=John Tate|year=1967}} on [[p-divisible group]]s, and named them Mumford–Tate groups.
What is the ideal knife for a bug out bag? There is no set answer but the ideal fixed bladed, high carbon, complete tang knife with a 3.5" - five" drop point tip that you can afford is usually offered as a answer. Nevertheless, possessing one knife for all your survival chores is a story of compromise.<br><br>In the event you adored this information along with you desire to get more info with regards to [http://www.thebestpocketknifereviews.com/best-multi-tool-survival-pocket-tool-review/ http://www.thebestpocketknifereviews.com/best-multi-Tool-survival-pocket-tool-review] i implore you to check out our web-page. The name of the firm has essentially altered, the knives are made to the exact same higher high quality specifications that George Schrade firmly insisted upon when he initially began creating them in 1904. There have been two versions made of the Important Each and every Day Carry Knife, a single with a stainless steel bolster and a single without the need of. Regardless of which one you select, you will be very pleased with the kind AND function of this excellent Every single Day Carry Knife! My nameCPT Jason Rissler, and I am a US Army Infantry Company Commander serving in Alaska. I have made use of and collected knives my complete adult life. As all soldiers do, I appreciate good quality and durability in all the tools I use on a daily basis in my expert life.<br><br>For sturdiness you definitely want to have a fixed blade knife in a sheath. There's much more to it than that, even though. Knives have what is called a “tang,” the metal part that continues previous the blade and into the handle. What you are searching for in a survival knife is a full tang, which [http://www.harrietoneilllaw.com/node/582395 suggests] that the metal from your blade extends all the way by way of to the bottom of the manage. This design and style makes for a nice, strong blade. Something less than this is likely to break on you during a hectic emergency circumstance.<br><br>It is expensive compared to other bushcraft knives The handle must give you comfort when handling the knife. Pick the one particular with sturdy and comfy manage. Some are created of wood, [http://sss.Chaoslab.ru/tracker/mim_plugs/newticket?reporter=anonymous&summary=AttributeError%3A+%27Environment%27+object+has+no+attribute+%27get_db_cnx%27&description=Oscillating+Multi-Tools+%28OMT%29+have+%5Bhttp%3A%2F%2FEsmikorea.ezconn.net%2Fxe%2F%3Fdocument_srl%3D70024+exploded%5D+in+recognition+and+produced+a+substantial+sector+of+the+power+tool+market.+These+%5Bhttp%3A%2F%2FAdvisory-Council.mol.go.th%2Fnode%2F33327+versatile+tools%5D+give+contractors%2C+renovators+and+DIY%27ers+a+go-to+alternative+for+a+variety+of+cutting%2C+grinding+and+sanding+applications+where+restricted+space+is+an+concern.++If+you+want+to+learn+more+regarding+%5Bhttp%3A%2F%2Fwww.thebestpocketknifereviews.com%2Fbest-multi-tool-survival-pocket-tool-review%2F+Best+Survival+Multi+Tool%5D+check+out+our+webpage.+Current+developments+in+battery+technology+have+allowed+the+tool+producers+to+create+cordless+OMT%27s+with+equivalent+energy+and+overall+performance+to+the+original+corded+versions.%0D%0A%0D%0A%0D%0A%0D%0AThe+Leatherman+Skeletool+is+my+choice+for+a+little+multitool.+Yes%2C+it%27s+four%22-closed%2C+but+it%27s+truly+slim+and+light.+With+its+pocket+clip%2C+it+carries+like+a+regular+pocket+knife.+Every+portion+is+solid+stainless+steel+or+reinforced+with+stainless.+This+higher+grade+metal+will+not+rust+even+when+immersed+in+water.+Leatherman+provides+a+25+year+warranty+on+all+its+items.+The+tool+is+4+inches+long+when+closed+and+weighs+approximately+8.5+ounces.+%28This+a+single+is+my+personal+favorite%21%29+The+pliers+are+a+compound+tool+and+exert+greater+mechanical+leverage+than+standard+hand+stress.+The+knife+is+modest+but+serrated+and+hugely+versatile.+The+saw+is+fine+and+difficult+sufficient+to+cut+by+means+of+copper+pipe.+Stainless+Steel+Locking+Multitool+Pliers+w%2F+Sheath+831102+Grout+removal+blades%0D%0A%0D%0AWe+also+wanted+to+mention+Victorinox%27s+SwissTool+%28from+the+makers+of+the+popular+Swiss+Army+Knife%29+and+CyberTool+%2C+which+many+of+you+nominated+for+the+reason+that+of+Victorinox%27s+reputation+and+history+for+nicely+crafted%2C+effectively+constructed+solutions.+Each+the+CyberTool+and+SwissTool+are+product+lines%2C+so+you+can+pick+the+multitool+that+has+the+quantity+of+person+tools+and+the+type+issue+that+you+happen+to+be+looking+for+and+operates+in+your+price+range.+The+SwissTool+is+commonly+regarded+as+a+far+more+all-goal%2C+multi-purpose+tool%2C+when+the+CyberTool+has+features+that+are+more+geared+towards+somebody+who%27ll+have+to+have+to+do+repairs+about+the+office+or+with+technology%E2%80%94like+the+inside+of+your+household-constructed+Computer.%0D%0A%0D%0AIt+is+notable+that+this+is+the+only+tool+in+this+group+that+does+not+use+an+18V+battery%2C+this+tool+runs+on+a+14.4V+platform.+This+is+yet+another+1+of+the+tools+that+does+not+function+a+work+light+in+it+is+style.+The+FEIN+AFMM+14+does+give+a+tool-absolutely+free+blade+change+%28FEIN+is+the+father+of+these+tools+and+the+tool-totally+free+design%21%29%2C+along+with+a+typical+on%2Foff+switch+and+variable+speed+dial.+The+tool-no+cost+blade+adjust+technique+uses+a+removable+pin%2Fbolt+that+holds+the+blades+in+position.%0D%0A%0D%0AThe+tools+are+accessible+devoid+of+obtaining+to+unfold+the+whole+tool+which+to+me+is+handy+when+attempting+to+do+factors+1+handed.+I+often+handle+to+start+off+factors+and+get+a+single+hand+busy+and+then+hunt+for+my+tools.+I+have+to+use+tools+that+match+my+impatient+nature+sometime+because+I+start+off+issues+and+then+have+to+catch+up+by+grabbing+a+tool+with+1+hand.+You+can+also+study+far+more+information+about+Gerber+22-41545+Black+Diesel+Multi-Plier+with+Sheath+tool+as-nicely.+I+did+start+out+this+project+applying+my+Dremel+Multi-Max+but+it+died+following+10+minutes.+This+truly+upset+me+considering+that+I+just+opened+and+applied+a+new+grout+attachment+%28which+expense+%2425%29.+Arrrrrrrgggghhhhhh.+Emergency+Travel+Tool+22-01769+Stainless+Steel+Tools++Pocketknife+Critique+SOG+Flash+Rescue+%2467.50+What+multitool+do+you+carry%3F%0D%0A%0D%0AYeah%2C+the+squirt+is+significantly+smaller+sized+than+it+appears+on+that+page.+I+also+second+the+Juice.+1+issue+with+the+Juice%2C+at+least+my+version%2C+is+that+the+flathead+blades+are+incredibly+complicated+to+pull+out.+They+are+jammed+in+there+fantastic.+A+multi-tool+might+not+replace+a+fantastic+toolbox%2C+but+I%27d+rather+carry+it+around.+A+knife+crafted+from+420HC%2C+a+higher-carbon+stainless+steel+that+is+corrosion+resistant+and+can+be+quickly+maintained.+A+stainless+steel+blank+coated+with+premium+synthetic+diamond+particles+which+develop+a+rough+surface+that+can+be+made+use+of+to+sharpen+difficult+steel+blades+with+a+great+deal+far+more+precision+than+wood%2Fmetal+files.+In+terms+of+price+tag%2C+we%27ve+seen+the+Gerber+600+retailed+for+roughly+%2440%2C+when+the+Leatherman+Wave+retails+for+around+%2460.%0D%0A%0D%0AI%27m+a+tool+guy.+I+always+have+been.+When+I+was+a+kid+I+was+notorious+for+taking+items+apart+and+%28often%29+having+them+back+with+each+other+once+again.+I+was+normally+developing+items+with+saws%2C+hammers%2C+drills%2C+nails+making+use+of+the+occasional+cost-free+sheet+of+plywood+that+would+fall+off+a+truck.+My+enjoy+of+tools+also+applies+to%2C+of+course%2C+hiking+and+backpacking.+What+follows+is+an+report+I%27m+positive+all+backpackers+can+identify+with+in+a+single+way+or+one+more.+Hopefully+my+recommendations+on+the+appropriate+option+for+backpacking+tools+make+sense+to+you+as+considerably+as+it+does+me.+My+Burmese+Machete&create=Create composite] components, and antler. Picture getting a knife created of low corrosion material, or a heavy one, I never think you can work comfortably. Blade sharpness A great bushcraft knife should really be versatile in the quantity of activities you can execute. Keep in mind when you are in the wild you require to carryout unique activities and it will be inconvenient or even hazardous if your knife can only do 1 or 2 points. You actuallyto get a universal job knife that can multitask. After all, all you want is an helpful survival knife, not just a knife. Fixed Blade Selections<br><br>I have made use of mine as other folks use their knives, what differs is that my Strider Knife gets place away prepared to go once again, other folks will need to be re-sharpened, a chip desires to be taken out of the blade or that bit of rust growing on the hand guard may possibly be going all the way down into the deal with, consuming into the tang. When I take out to use my knife, I never have any question whether or not it will do what I am asking of it. 100% self-assurance. 1st, there is the knife. Absolutely nothing spectacular right here, though the blade is extremely fantastic at holding an edge, and functions good for every thing from skinning catfish to scaling bluegill to skinning & quartering wild hogs. I under no circumstances heard of S30V stainless ahead of I handled this knife, but I now know that it is extremely superior stuff.<br><br>The Columbia River Knife and Tool (CRKT) company makes a full line of pretty nice, reasonably priced knives. Most of these are folders, but really protected folders. They have a double locking mechanism that tends to make them as close to a fixed blade knife as you can get in a folder. I hold one of them, from the M16 line, in my PFD survival kit Plaza Cutlery, a family members owned business enterprise, is a single of the finest cutlery shops in the planet. It supply new knives as soon as they are available and is often nicely stocked. In addition to factory-produced folding knives, fixed blade and specialty knives, Plaza Cutlery also carries a significant choice of custom knives. The blade of this knife came very sharp and is simple to touch up with the Bear Grylls field sharpener. Blade Length (inches)<br><br>The knife pictured in Fig 12 is a Bowie Knife created by mountain man/frontiersman/politician Jim Bowie. In years previous mountain men utilized single shot muzzleloaders and if that one particular shot was not sufficient to bring down a charging bear a knife was necessary to finish the job. A person required a large sharp knife that could plunge deep into the hard hide of a bear, mountain lion or human aggressor. Stainless steel grades for knife blades typically start off at 400 and run thru 425 and the higher the quantity the greater grade of steel. Measuring just over 11 inches in complete length, ten to 12 inches getting the excellent length for survival knives, the Fallkniven A1 capabilities a full length tang which normally makes for a stronger blade. Click right here for prices, images and reviews<br><br>The Schrade Deerslayer is among these regular Schrade knives that created the brand name so popular. Today's variation is nevertheless really powerful and a rather common skinning knife. I carried and used a Randall #14 for years, by no means had a single issue with it, how I found Strider Knives was I was looking for a nylon sheath for my Randall #14, saw the type of sheath MickDuane have been working with for their knives and thought if they put this a great deal thought into the sheath, what is the knife like? 2004 OKCA Best Hunting/Utility Knife Next, there's a gut hook. To access it, you press the bolster lock and pivot the knife handle 180 degrees. Voila! Now the blade is safely encased in the deal with, and you have a gut hook of enormous size and superior design and style at your disposal.<br><br>For the size and weight of a enormous folder, you can pocket a knife that can do virtually anything the giant folder can with numerous fewer troubles. Provided you use them in the right spot, a fixed blade can do effectively as an EDC knife. Give one a try and you may possibly just swear off an Espada forever. Okay, possibly not–you can carry one particular to go with your Halloween costume in a few months. Connected The blade is heavy but I prefer a heavy blade versus a heavy deal with where the blade is so light it actually rises when holding the knife by the deal with. Fantastic overall balance and it is a knife you must have in your survival pack. Carry a single in the auto, preserve 1 at home and pack one particular out when you head out for some wilderness adventure. Folding Knives in a Survival Situation
 
==Formulation==
The algebraic torus ''T'' used to describe Hodge structures has a concrete matrix representation, as the 2&times;2 invertible matrices of the shape that is given by the action of ''a''+''bi'' on the basis {1,''i''} of the complex numbers '''C''' over '''R''':
 
:<math>\begin{bmatrix} a & b \\ -b & a \end{bmatrix}.
      </math>
 
The circle group inside this group of matrices is the [[unitary group]] ''U''(1).
 
Hodge structures arising in geometry, for example on the [[cohomology group]]s of [[Kähler manifold]]s, have a [[lattice (group theory)|lattice]] consisting of the integral cohomology classes. Not quite so much is needed for the definition of the Mumford&ndash;Tate group, but it does assume that the vector space ''V'' underlying the Hodge structure has a given rational structure, i.e. is given over the rational numbers ''Q''. For the purposes of the theory the complex vector space ''V''<sub>''C''</sub>, obtained by extending the scalars of ''V'' from ''Q'' to ''C'', is used.
 
The weight ''k'' of the Hodge structure describes the action of the diagonal matrices of ''T'', and ''V'' is supposed therefore to be homogeneous of weight ''k'', under that action. Under the action of the full group ''V''<sub>''C''</sub> breaks up into subspaces ''V''<sup>''pq''</sup>, complex conjugate in pairs under switching ''p'' and ''q''. Thinking of the matrix in terms of the complex number &lambda; it represents, ''V''<sup>''pq''</sup> has the action of &lambda; by the ''p''th power and of the complex conjugate of &lambda; by the ''q''th power. Here necessarily
 
:''p'' + ''q'' = ''k''.
 
In more abstract terms, the torus ''T'' underlying the matrix group is the [[Weil restriction]] of the [[multiplicative group]] ''GL''(1), from the complex field to the real field, an algebraic torus whose character group consists of the two homomorphisms to ''GL''(1), interchanged by complex conjugation.
 
Once formulated in this fashion, the rational representation &rho; of ''T'' on ''V'' setting up the Hodge structure ''F'' determines the image &rho;(''U''(1)) in ''GL''(''V''<sub>''C''</sub>); and ''MT''(''F'') is by definition the Zariski closure, for the ''Q''-Zariski topology on ''GL''(''V''), of this image.<ref>http://www.math.columbia.edu/~thaddeus/seattle/voisin.pdf, pp. 7&ndash;9.</ref>
 
==Mumford–Tate conjecture==
 
The original context for the formulation of the group in question was the question of the [[Galois representation]] on the [[Tate module]] of an [[abelian variety]] ''A''. Conjecturally, the image of such a Galois representation, which is an [[l-adic]] Lie group for a given prime number ''l'', is determined by the corresponding Mumford–Tate group ''G'' (coming from the Hodge structure on ''H''<sup>1</sup>(''A'')), to the extent that knowledge of ''G'' determines the [[Lie algebra]] of the Galois image. This conjecture is known only in particular cases.<ref>http://math.berkeley.edu/~ribet/Articles/mg.pdf, survey by [[Ken Ribet]].</ref> Through generalisations of this conjecture, the Mumford–Tate group has been connected to the [[motivic Galois group]], and, for example, the general issue of extending the [[Sato&ndash;Tate conjecture]] (now a theorem).
 
==Period conjecture==
 
A related conjecture on abelian varieties states that the [[period matrix]] of ''A'' over number field has [[transcendence degree]], in the sense of the field generated by its entries, predicted by the dimension of its Mumford&ndash;Tate group, as in the previous section. Work of [[Pierre Deligne]] has shown that the dimension bounds the transcendence degree; so that the Mumford&ndash;Tate group catches sufficiently many algebraic relations between the periods. This is a special case of the full Grothendieck period conjecture.<ref>http://math.cts.nthu.edu.tw/Mathematics/preprints/prep2005-6-002.pdf, p. 3.</ref><ref>http://arxiv.org/abs/0805.2569v1, p. 7.</ref>
 
==Notes==
{{reflist}}
 
==References==
 
*{{Citation | last1=Mumford | first1=David | author1-link=David Mumford | title=Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) | publisher=[[American Mathematical Society]] | location=Providence, R.I. | id={{MR|0206003}} | year=1966 | chapter=Families of abelian varieties | pages=347–351}}
*{{Citation | last1=Serre | first1=Jean-Pierre | author1-link=Jean-Pierre Serre | editor1-last=Springer | editor1-first=Tonny A. | title=Proceedings of a Conference on Local Fields  (Driebergen, 1966) | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-03953-2 | id={{MR|0242839}} | year=1967 | chapter=Sur les groupes de Galois attachés aux groupes p-divisibles | pages=118–131}}
*{{Citation | last1=Tate | first1=John T. | editor1-last=Springer | editor1-first=Tonny A. | title=Proc. Conf. Local Fields( Driebergen, 1966) | publisher=[[Springer-Verlag]] | location=Berlin, New York | mr=0231827 | year=1967 | chapter=p-divisible groups.}}
 
==External links==
*[http://www.math.umass.edu/~hacking/agnes/griffiths.pdf Lecture slides (PDF)] by [[Phillip Griffiths]]
*[http://www.cms.zju.edu.cn/UploadFiles/AttachFiles/2005730145725232.pdf ''Mumford-Tate groups, families of Calabi-Yau varieties and analogue André-Oort problems I'', preprint (PDF)]
 
{{DEFAULTSORT:Mumford-Tate group}}
[[Category:Hodge theory]]
[[Category:Algebraic groups]]

Latest revision as of 20:49, 21 August 2014

What is the ideal knife for a bug out bag? There is no set answer but the ideal fixed bladed, high carbon, complete tang knife with a 3.5" - five" drop point tip that you can afford is usually offered as a answer. Nevertheless, possessing one knife for all your survival chores is a story of compromise.

In the event you adored this information along with you desire to get more info with regards to http://www.thebestpocketknifereviews.com/best-multi-Tool-survival-pocket-tool-review i implore you to check out our web-page. The name of the firm has essentially altered, the knives are made to the exact same higher high quality specifications that George Schrade firmly insisted upon when he initially began creating them in 1904. There have been two versions made of the Important Each and every Day Carry Knife, a single with a stainless steel bolster and a single without the need of. Regardless of which one you select, you will be very pleased with the kind AND function of this excellent Every single Day Carry Knife! My nameCPT Jason Rissler, and I am a US Army Infantry Company Commander serving in Alaska. I have made use of and collected knives my complete adult life. As all soldiers do, I appreciate good quality and durability in all the tools I use on a daily basis in my expert life.

For sturdiness you definitely want to have a fixed blade knife in a sheath. There's much more to it than that, even though. Knives have what is called a “tang,” the metal part that continues previous the blade and into the handle. What you are searching for in a survival knife is a full tang, which suggests that the metal from your blade extends all the way by way of to the bottom of the manage. This design and style makes for a nice, strong blade. Something less than this is likely to break on you during a hectic emergency circumstance.

It is expensive compared to other bushcraft knives The handle must give you comfort when handling the knife. Pick the one particular with sturdy and comfy manage. Some are created of wood, composite components, and antler. Picture getting a knife created of low corrosion material, or a heavy one, I never think you can work comfortably. Blade sharpness A great bushcraft knife should really be versatile in the quantity of activities you can execute. Keep in mind when you are in the wild you require to carryout unique activities and it will be inconvenient or even hazardous if your knife can only do 1 or 2 points. You actuallyto get a universal job knife that can multitask. After all, all you want is an helpful survival knife, not just a knife. Fixed Blade Selections

I have made use of mine as other folks use their knives, what differs is that my Strider Knife gets place away prepared to go once again, other folks will need to be re-sharpened, a chip desires to be taken out of the blade or that bit of rust growing on the hand guard may possibly be going all the way down into the deal with, consuming into the tang. When I take out to use my knife, I never have any question whether or not it will do what I am asking of it. 100% self-assurance. 1st, there is the knife. Absolutely nothing spectacular right here, though the blade is extremely fantastic at holding an edge, and functions good for every thing from skinning catfish to scaling bluegill to skinning & quartering wild hogs. I under no circumstances heard of S30V stainless ahead of I handled this knife, but I now know that it is extremely superior stuff.

The Columbia River Knife and Tool (CRKT) company makes a full line of pretty nice, reasonably priced knives. Most of these are folders, but really protected folders. They have a double locking mechanism that tends to make them as close to a fixed blade knife as you can get in a folder. I hold one of them, from the M16 line, in my PFD survival kit Plaza Cutlery, a family members owned business enterprise, is a single of the finest cutlery shops in the planet. It supply new knives as soon as they are available and is often nicely stocked. In addition to factory-produced folding knives, fixed blade and specialty knives, Plaza Cutlery also carries a significant choice of custom knives. The blade of this knife came very sharp and is simple to touch up with the Bear Grylls field sharpener. Blade Length (inches)

The knife pictured in Fig 12 is a Bowie Knife created by mountain man/frontiersman/politician Jim Bowie. In years previous mountain men utilized single shot muzzleloaders and if that one particular shot was not sufficient to bring down a charging bear a knife was necessary to finish the job. A person required a large sharp knife that could plunge deep into the hard hide of a bear, mountain lion or human aggressor. Stainless steel grades for knife blades typically start off at 400 and run thru 425 and the higher the quantity the greater grade of steel. Measuring just over 11 inches in complete length, ten to 12 inches getting the excellent length for survival knives, the Fallkniven A1 capabilities a full length tang which normally makes for a stronger blade. Click right here for prices, images and reviews

The Schrade Deerslayer is among these regular Schrade knives that created the brand name so popular. Today's variation is nevertheless really powerful and a rather common skinning knife. I carried and used a Randall #14 for years, by no means had a single issue with it, how I found Strider Knives was I was looking for a nylon sheath for my Randall #14, saw the type of sheath MickDuane have been working with for their knives and thought if they put this a great deal thought into the sheath, what is the knife like? 2004 OKCA Best Hunting/Utility Knife Next, there's a gut hook. To access it, you press the bolster lock and pivot the knife handle 180 degrees. Voila! Now the blade is safely encased in the deal with, and you have a gut hook of enormous size and superior design and style at your disposal.

For the size and weight of a enormous folder, you can pocket a knife that can do virtually anything the giant folder can with numerous fewer troubles. Provided you use them in the right spot, a fixed blade can do effectively as an EDC knife. Give one a try and you may possibly just swear off an Espada forever. Okay, possibly not–you can carry one particular to go with your Halloween costume in a few months. Connected The blade is heavy but I prefer a heavy blade versus a heavy deal with where the blade is so light it actually rises when holding the knife by the deal with. Fantastic overall balance and it is a knife you must have in your survival pack. Carry a single in the auto, preserve 1 at home and pack one particular out when you head out for some wilderness adventure. Folding Knives in a Survival Situation