Counterexample to Néron-Ogg-Shafarevich criterion for Calabi-Yau threefolds
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910501527617536 |
|---|---|
| author | Chmiel, Tymoteusz Oczko, Marcin |
| author_facet | Chmiel, Tymoteusz Oczko, Marcin |
| contents | For any prime $p>5$ we construct a Calabi-Yau threefold $X$ defined over a finite extension $K$ of $\mathbb{Q}_p$ such that every model of $X$ over $\operatorname{Spec}\mathcal{O}_K$ has singular special fiber, yet the Galois action on the $\ell$-adic cohomology group $H^3_{\acute{e}t}(X,\mathbb{Q}_\ell)$ is unramified for $\ell\neq p$ and crystalline for $\ell=p$. This provides a counterexample to the analogue of the Néron-Ogg-Shafarevich criterion for three-dimensional Calabi-Yau manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04008 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Counterexample to Néron-Ogg-Shafarevich criterion for Calabi-Yau threefolds Chmiel, Tymoteusz Oczko, Marcin Algebraic Geometry For any prime $p>5$ we construct a Calabi-Yau threefold $X$ defined over a finite extension $K$ of $\mathbb{Q}_p$ such that every model of $X$ over $\operatorname{Spec}\mathcal{O}_K$ has singular special fiber, yet the Galois action on the $\ell$-adic cohomology group $H^3_{\acute{e}t}(X,\mathbb{Q}_\ell)$ is unramified for $\ell\neq p$ and crystalline for $\ell=p$. This provides a counterexample to the analogue of the Néron-Ogg-Shafarevich criterion for three-dimensional Calabi-Yau manifolds. |
| title | Counterexample to Néron-Ogg-Shafarevich criterion for Calabi-Yau threefolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2309.04008 |