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| In the mathematical field of [[algebraic topology]], a '''commutative ring spectrum''', roughly equivalent to a [[E-infinity ring spectrum|<math>E_\infty</math>-ring spectrum]], is a [[commutative monoid]] in a good<ref>symmetric monoidal with respect to [[smash product]] and perhaps some other conditions; one choice is the category of [[symmetric spectrum|symmetric spectra]]</ref> category of [[spectrum (topology)|spectra]].
| | I'm Joyce (25) from Weilbach, Austria. <br>I'm learning Turkish literature at a local college and I'm just about to graduate.<br>I have a part time job in a backery.<br><br>Here is my weblog: korean women ([http://bestbreastfirmingcream.com just click the following website]) |
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| The category of commutative ring spectra over the field <math>\mathbb{Q}</math> of rational numbers is [[Quillen equivalent]] to the cateogy of [[differential graded algebra]]s over <math>\mathbb{Q}</math>.
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| Example: The [[Witten genus]] may be realized as a [[morphism]] of commutative ring spectra [[MString]] →'''[[tmf]]'''.
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| See also: [[simplicial commutative ring]], [[highly structured ring spectrum]] and [[derived scheme]].
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| == Terminology ==
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| Almost all reasonable categories of commutative ring spectra can be shown to be [[Quillen equivalent]] to each other. Thus, from the point view of the [[stable homotopy theory]], the term "commutative ring spectrum" may be used as a synonymous to an <math>E_\infty</math>-ring spectrum.
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| == Notes ==
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| {{reflist}}
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| == References ==
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| * P. Goerss, [http://www.math.northwestern.edu/~pgoerss/papers/Exp.1005.P.Goerss.pdf Topological Modular Forms <nowiki>[after Hopkins, Miller, and Lurie]</nowiki>]
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| * J.P. May, What precisely are <math>E_\infty</math> ring spaces and <math>E_\infty</math> ring spectra? {{arxiv|0903.2813}}
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| {{topology-stub}}
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| [[Category:Algebraic topology]]
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Latest revision as of 03:55, 3 October 2014
I'm Joyce (25) from Weilbach, Austria.
I'm learning Turkish literature at a local college and I'm just about to graduate.
I have a part time job in a backery.
Here is my weblog: korean women (just click the following website)