Galois equivariance and stable motivic homotopy theory
| Autor: | Jeremiah Heller, Kyle Ormsby |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Pure mathematics Functor Brown's representability theorem Homotopy category Applied Mathematics General Mathematics Homotopy 010102 general mathematics Galois group Mathematics::Algebraic Topology 01 natural sciences Embedding problem Mathematics::K-Theory and Homology Adams spectral sequence Mathematics::Category Theory 0103 physical sciences 010307 mathematical physics Galois extension 0101 mathematics Mathematics |
| Zdroj: | Transactions of the American Mathematical Society. 368:8047-8077 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/tran6647 |
| Popis: | For a finite Galois extension of fields L/k with Galois group G, we study a functor from the G-equivariant stable homotopy category to the stable motivic homotopy category over k induced by the classical Galois correspondence. We show that after completing at a prime and η (the motivic Hopf map) this results in a full and faithful embedding whenever k is real closed and L = k[i]. It is a full and faithful embedding after η-completion if a motivic version of Serre’s finiteness theorem is valid. We produce strong necessary conditions on the field extension L/k for this functor to be full and faithful. Along the way, we produce several results on the stable C2-equivariant Betti realization functor and prove convergence theorems for the p-primary C2-equivariant Adams spectral sequence. |
| Databáze: | OpenAIRE |
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