• Source: 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




π

∗


F
→

π

∗


G


{\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.

Kata Kunci Pencarian:

• Sheaf of spectra
• Sheaf (mathematics)
• Ringed space
• Spectrum of a ring
• Perfect complex
• Cohomology
• Landweber exact functor theorem
• Topological modular forms
• A¹ homotopy theory
• Analytic space