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 FG is a weak equivalence if the induced map of homotopy sheaves 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

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


    This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.