On Tate Milnor-Witt Motives
Jean Fasel, Nanjun Yang

TL;DR
This paper studies Tate Milnor-Witt motives associated with smooth projective G_m-varieties, providing a splitting formula over Euclidean fields that simplifies their Chow-Witt group computations.
Contribution
It introduces a splitting formula for Tate Milnor-Witt motives over Euclidean fields, linking Chow-Witt groups to Chow groups and Witt sheaf cohomologies.
Findings
Tate Milnor-Witt motives exist for certain smooth projective G_m-varieties.
A splitting formula reduces Chow-Witt group calculations to more manageable invariants.
The approach applies to varieties with isolated rational fixed points.
Abstract
Smooth projective -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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Topological and Geometric Data Analysis · History and Theory of Mathematics
