Cup product of inhomogeneous Tate cochains, and Galois cohomology of tori over local fields that split over cyclic extensions
Abstract
In this note we give formulas for cup product in Tate cohomology in terms of inhomogeneous cochains. Using one of these formulas, for a torus T defined over a non-archimedean local field K and splitting over a cyclic extension of K, we compute explicit cocycles representing all cohomology classes in H^1(K,T).
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Geometric and Algebraic Topology
Publication details
- Journal / source
- Communications in Mathematics
- Volume
- Volume 34 (2026), Issue 1
- Publication date
- 8 July 2026
- Language
- EN