Sheaf of spectra

In algebraic topology, a presheaf of spectra on a 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 ${\displaystyle \pi _{*}F\to \pi _{*}G}$ 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 in algebraic geometry.

References

External links

• Goerss, Paul (16 June 2008). "Schemes" (PDF). TAG Lecture 2.

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This page was last edited on 1 April 2021, at 10:04