Mikhail Borovoi - Cup product of inhomogeneous Tate cochains, and Galois cohomology of tori over local fields that split over cyclic extensions

cm:17416 - Communications in Mathematics, July 8, 2026, Volume 34 (2026), Issue 1 - https://doi.org/10.46298/cm.17416
Cup product of inhomogeneous Tate cochains, and Galois cohomology of tori over local fields that split over cyclic extensionsArticle

Authors: Mikhail Borovoi

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).

https://doi.org/10.46298/cm.17416
Source: arXiv.org:2508.07288
Volume: Volume 34 (2026), Issue 1
Published on: July 8, 2026
Accepted on: June 23, 2026
Submitted on: January 28, 2026
Keywords: Number Theory, Group Theory, Representation Theory, 11E72, 11R37, 11S, 20G10, 20G25, 20J06
Licence: Attribution 4.0 International (CC BY 4.0)

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