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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.

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
© 2025 MSP (Mathematical Sciences Publishers).