Galois equivariance and stable motivic homotopy theory

Autor:	Heller, J., Ormsby, K.
Rok vydání:	2014
Předmět:	Mathematics - Algebraic Topology Mathematics - Algebraic Geometry Primary: 14F42 55P91 Secondary: 11E81 19E15
Druh dokumentu:	Working Paper
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 eta (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 eta-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 C_2-equivariant Betti realization functor and prove convergence theorems for the p-primary C_2-equivariant Adams spectral sequence. Comment: 28 pages; v3: several corrections, main theorem updated, convergence proofs added. Accepted for publication in Transactions of the AMS
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1401.4728 Zobrazit plný text záznamu View this record from Arxiv