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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.07979 |
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| _version_ | 1866911952385605632 |
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| author | Lüders, Morten |
| author_facet | Lüders, Morten |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07979 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $p$-adic tame Tate twists Lüders, Morten Algebraic Geometry 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. |
| title | $p$-adic tame Tate twists |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.07979 |