References & Citations
Mathematics > Algebraic Geometry
Title: Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer
(Submitted on 5 Jul 2020 (v1), last revised 19 Apr 2024 (this version, v3))
Abstract: In this paper, we develop a theory of Becker-Gottlieb transfer based on Spanier-Whitehead duality that holds in both the motivic and \'etale 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 \'etale 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.
Submission history
From: Roy Joshua [view email][v1] Sun, 5 Jul 2020 06:23:39 GMT (90kb)
[v2] Sat, 22 Aug 2020 20:46:07 GMT (90kb)
[v3] Fri, 19 Apr 2024 20:24:45 GMT (67kb)
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