View source for Sheaf of spectra

{{Citations|date=March 2015}}
In algebraic topology, a '''presheaf of spectra''' on a [[Topological space|topological space]] ''X'' is a contravariant functor from the category of open subsets of ''X'', where morphisms are inclusions, to the good category of commutative ring spectra. A theorem of Jardine says that such presheaves form a simplicial model category, where ''F'' →''G'' is a weak equivalence if the induced map of homotopy sheaves <math>\pi_* F \to \pi_* G</math> is an isomorphism. A '''sheaf of spectra''' is then a fibrant/cofibrant object in that category.

The notion is used to define, for example, a [[Derived scheme|derived scheme]] in algebraic geometry.

==References==
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==External links==
*{{cite web |url=http://www.math.ku.dk/~jg/homotopical2008/goerss.lec2.pdf |first=Paul |last=Goerss |title=Schemes |work=TAG Lecture 2 |date=16 June 2008 }}

[[Category:Algebraic topology]]



{{Sourceattribution|Sheaf of spectra}}