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On Tate Milnor–Witt motives

Jean Fasel and Nanjun Yang
Vol. 10 (2025), No. 2, 153–187
DOI: 10.2140/akt.2025.10.153
Abstract

Smooth projective 𝔾m-varieties with isolated rational fixed points admit Tate Milnor–Witt motives. Over Euclidean fields, we give a splitting formula of such motives, which reduces the computation of their Chow–Witt groups to that of their Chow groups and cohomologies of Witt sheaf.

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Keywords
Milnor–Witt motives, higher Bocksteins, cellular varieties
Mathematical Subject Classification
Primary: 14F42
Secondary: 55T25
Milestones
Received: 17 June 2024
Revised: 5 March 2025
Accepted: 30 March 2025
Published: 30 April 2025
Authors
Jean Fasel
Institut Fourier – UMR 5582
Université Grenoble Alpes
CNRS
CS 40700
38058 Grenoble Cedex 9
France
Nanjun Yang
Beijing Institute of Mathematical Sciences and Applications
Huairou District
Beijing
China
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