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arXiv · 2407.07979

$p$-adic tame Tate twists

Morten Lüders
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Abstract

Recently, Hübner-Schmidt defined the tame site of a scheme. We define $p$-adic tame Tate twists in the tame topology and prove some first properties. We establish a framework analogous to the Beilinson-Lichtenbaum conjectures in the tame topology for $p$-adic tame Tate twists and tame logarithmic deRham-Witt sheaves. Both only differ from their étale counterpart in cohomological degrees above the weight. These cohomology groups can be analysed using the Gersten conjecture which, at least conjecturally, has a nice shape in the tame topology. We prove the Gersten conjecture for tame logarithmic deRham-Witt sheaves for curves in positive characteristic and note that the conjecture in arbitrary dimension would follow from strict $\mathbb{A}^1$-invariance.

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Morten Lüders. 2024-07-10. $p$-adic tame Tate twists. https://arxiv.org/abs/2407.07979

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