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arXiv · 2508.07288

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

Mikhail Borovoi
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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).

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Mikhail Borovoi. 2025-08-10. Cup product of inhomogeneous Tate cochains, and Galois cohomology of tori over local fields that split over cyclic extensions. https://doi.org/10.46298/cm.17416

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