Commutative ring spectrum

In <a href="/facts/Algebraic_topology/2wA8yrjT">algebraic topology</a>, a commutative ring spectrum, roughly equivalent to a <a href="/facts/E-infinity_ring_spectrum/GC2bU7L7">
 
 
 
 
 E
 
 ∞
 
 
 
 
 {\displaystyle E_{\infty }}
 
-ring spectrum</a>, is a <a href="/facts/Commutative_monoid/6AHve7p8">commutative monoid</a> in a good category of <a href="/facts/Spectrum_(topology)/mWho3roy">spectra</a>.
The category of commutative ring spectra over the field 
 
 
 
 
 Q
 
 
 
 {\displaystyle \mathbb {Q} }
 
 of rational numbers is <a href="/facts/Quillen_equivalent/QD5MCczK">Quillen equivalent</a> to the category of <a href="/facts/Differential_graded_algebra/zySud4Kl">differential graded algebras</a> over 
 
 
 
 
 Q
 
 
 
 {\displaystyle \mathbb {Q} }
 
.
Example: The <a href="/facts/Witten_genus/bUM7KXJ0">Witten genus</a> may be realized as a <a href="/facts/Morphism/Kdpuyz3S">morphism</a> of commutative ring spectra MString →<a href="/facts/Topological_modular_forms/VUCg7KHN">tmf</a>.
See also: <a href="/facts/Simplicial_commutative_ring/6LktuDH8">simplicial commutative ring</a>, <a href="/facts/Highly_structured_ring_spectrum/GC2bU7L7">highly structured ring spectrum</a> and <a href="/facts/Derived_scheme/GbKo8lxS">derived scheme</a>.

Commutative ring spectrum open-in-new

Commutative ring spectrum