Reduction modulo $p$ of the Noether problem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914105277808640 |
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| author | Ambrosi, Emiliano Valloni, Domenico |
| author_facet | Ambrosi, Emiliano Valloni, Domenico |
| contents | Let $R$ be a complete valuation ring of mixed characteristic $(0,p)$ with algebraically closed fraction field $K$ and residue field $k$. Let $X/R$ be a smooth projective morphism. We show that if $X_k$ is stably rational, then $H^3(X_K, \mathbb Z_p)$ is torsion-free. The proof uses integral $p$-adic Hodge theory of Bhatt-Morrow-Scholze and the study of differential forms in positive characteristic. We then apply this result to study the Noether problem for finite $p$-groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_04153 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reduction modulo $p$ of the Noether problem Ambrosi, Emiliano Valloni, Domenico Algebraic Geometry Number Theory Let $R$ be a complete valuation ring of mixed characteristic $(0,p)$ with algebraically closed fraction field $K$ and residue field $k$. Let $X/R$ be a smooth projective morphism. We show that if $X_k$ is stably rational, then $H^3(X_K, \mathbb Z_p)$ is torsion-free. The proof uses integral $p$-adic Hodge theory of Bhatt-Morrow-Scholze and the study of differential forms in positive characteristic. We then apply this result to study the Noether problem for finite $p$-groups. |
| title | Reduction modulo $p$ of the Noether problem |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2302.04153 |