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arXiv · 2603.21681

Explicit isomorphisms for a Herr-type complex over a metabelian extension

Anand Chitrao·Aditya Karnataki·Jishnu Ray
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Abstract

Let $S$ be a Banach algebra over $\mathbb{Q}_p$ whose residue fields are finite extensions of $\mathbb{Q}_p$. Given an arithmetic family $V$ of Galois representations, i.e., a finite free $S$-module $V$ with a continuous action of the absolute Galois group of a $p$-adic number field, we construct a complex associated to $V$ over false-Tate extensions and construct explicit isomorphisms between its cohomology and the Galois cohomology. This recovers earlier results by Tavares Ribeiro when $S$ is a finite extension of $\mathbb{Q}_p$.

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Anand Chitrao, Aditya Karnataki, Jishnu Ray. 2026-03-23. Explicit isomorphisms for a Herr-type complex over a metabelian extension. https://arxiv.org/abs/2603.21681

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