Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer

Fuente: arXiv
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Autori principali: Carlsson, Gunnar, Joshua, Roy
Natura: Preprint
Pubblicazione: 2020
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author Carlsson, Gunnar
Joshua, Roy
author_facet Carlsson, Gunnar
Joshua, Roy
contents In this paper, we develop a theory of Becker-Gottlieb transfer based on Spanier-Whitehead duality that holds in both the motivic and étale settings for smooth quasi-projective varieties in as broad a context as possible: for example, for varieties over non-separably closed fields in all characteristics, and also for both the étale and motivic settings. In view of the fact that the most promising applications of the traditional Becker-Gottlieb transfer has been to torsors and Borel-style equivariant cohomology theories, we focus our applications to motivic cohomology theories for torsors as well as Borel-style equivariant motivic cohomology theories, both defined with respect to motivic spectra. We obtain several results in this direction, including a stable splitting in generalized motivic cohomology theories. Various further applications will be discussed in forthcoming papers.
format Preprint
id arxiv_https___arxiv_org_abs_2007_02247
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer
Carlsson, Gunnar
Joshua, Roy
Algebraic Geometry
14F20, 14F42, 14L30
In this paper, we develop a theory of Becker-Gottlieb transfer based on Spanier-Whitehead duality that holds in both the motivic and étale settings for smooth quasi-projective varieties in as broad a context as possible: for example, for varieties over non-separably closed fields in all characteristics, and also for both the étale and motivic settings. In view of the fact that the most promising applications of the traditional Becker-Gottlieb transfer has been to torsors and Borel-style equivariant cohomology theories, we focus our applications to motivic cohomology theories for torsors as well as Borel-style equivariant motivic cohomology theories, both defined with respect to motivic spectra. We obtain several results in this direction, including a stable splitting in generalized motivic cohomology theories. Various further applications will be discussed in forthcoming papers.
title Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer
topic Algebraic Geometry
14F20, 14F42, 14L30
url https://arxiv.org/abs/2007.02247