Stable etale realization and etale cobordism
| Autor: | Gereon Quick |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Mathematics(all)
Étale topological type Algebraic cobordism General Mathematics Étale cohomology Mathematics::Algebraic Topology Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Mathematics::K-Theory and Homology Mathematics::Category Theory FOS: Mathematics Algebraically closed field Algebraic Geometry (math.AG) Mathematics 14F42 Functor 14F45 14F35 (primary) 55P42 (secondary) Homotopy Cobordism Profinite spaces Stable homotopy theory Algebra Spectral sequence A1-homotopy theory of schemes Stable model structure |
| DOI: | 10.48550/arxiv.math/0608313 |
| Popis: | We show that there is a stable homotopy theory of profinite spaces and use it for two main applications. On the one hand we construct an \'etale topological realization of the stable motivic homotopy theory of smooth schemes over a base field of arbitrary characteristic in analogy to the complex realization functor for fields of characteristic zero. On the other hand we get a natural setting for \'etale cohomology theories. In particular, we define and discuss an \'etale topological cobordism theory for schemes. It is equipped with an Atiyah-Hirzebruch spectral sequence starting from \'etale cohomology. Finally, we construct maps from algebraic to \'etale cobordism and discuss algebraic cobordism with finite coefficients over an algebraically closed field after inverting a Bott element. Comment: 33 pages; minor corrections in section 3; to appear in Advances |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|