Une conjecture $C_{\rm st}$ pour la cohomologie à support compact
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908872824848384 |
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| author | Colmez, Pierre Gilles, Sally Nizioł, Wiesława |
| author_facet | Colmez, Pierre Gilles, Sally Nizioł, Wiesława |
| contents | Let $\mathbf{B}$ be the ring of analytic functions on the Fargues-Fontaine curve $Y_{\rm FF}$. We show that adding $p$-adic analogs of $\log p$ and $\log 2πi$ kills its Galois cohomology in degrees~$\geq 1$. The analogous result for $\mathbf{B}^+_{\rm dR}$ is folklore. This makes it possible to formulate $C_{\rm dR}$ and $C_{\rm st}$-type conjectures for compact support cohomology of $p$-adic analytic varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14675 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Une conjecture $C_{\rm st}$ pour la cohomologie à support compact Colmez, Pierre Gilles, Sally Nizioł, Wiesława Algebraic Geometry Number Theory Let $\mathbf{B}$ be the ring of analytic functions on the Fargues-Fontaine curve $Y_{\rm FF}$. We show that adding $p$-adic analogs of $\log p$ and $\log 2πi$ kills its Galois cohomology in degrees~$\geq 1$. The analogous result for $\mathbf{B}^+_{\rm dR}$ is folklore. This makes it possible to formulate $C_{\rm dR}$ and $C_{\rm st}$-type conjectures for compact support cohomology of $p$-adic analytic varieties. |
| title | Une conjecture $C_{\rm st}$ pour la cohomologie à support compact |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2511.14675 |