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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.07294 |
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| _version_ | 1866908947889258496 |
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| author | Kim, Taewan Ryu, Seunghun |
| author_facet | Kim, Taewan Ryu, Seunghun |
| contents | 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 Teichmüller 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 $γ-u^{-m}$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07294 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the cohomology of negative Tate twists via cyclotomic descent Kim, Taewan Ryu, Seunghun Number Theory 11R34 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 Teichmüller 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 $γ-u^{-m}$, 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. |
| title | On the cohomology of negative Tate twists via cyclotomic descent |
| topic | Number Theory 11R34 |
| url | https://arxiv.org/abs/2604.07294 |