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arXiv · 2604.07294

On the cohomology of negative Tate twists via cyclotomic descent

Taewan Kim·Seunghun Ryu
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Abstract

We show that the Galois cohomology of negative Tate twists can be organized by a single universal cyclotomic complex over the cyclotomic tower of $\mathbb{Q}$. Using cyclotomic descent and Teichm\"uller branch decomposition, we prove that a negative twist contributes only on the corresponding branch and is recovered by specializing the Iwasawa variable at a single point; equivalently, it is computed as the fiber of $\gamma-u^{-m}$, or $T=u^{-m}-1$ in Iwasawa coordinates. In the case $\mathbb{Q}_p/\mathbb{Z}_p$, this gives explicit descriptions of $H^1$ and $H^2$ in terms of the quotient and torsion of the $S$-ramified Iwasawa module.

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Taewan Kim, Seunghun Ryu. 2026-04-08. On the cohomology of negative Tate twists via cyclotomic descent. https://arxiv.org/abs/2604.07294

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