Torsion graded pieces of Nyggard filtration for crystalline representation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908886465773568 |
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| author | Liu, Tong |
| author_facet | Liu, Tong |
| contents | Let $K$ be a unramified $p$-adic field with the absolute Galois group $G_K$ and $T$ a crystalline $\mathbb Z_p$-representation of $G_K$. We study the graded pieces of integral filtration on $D_{\rm dR}(T)$ given by Nyggard filtration of the attached Breuil-Kisin module of $T$. We show that the $i$-graded piece has nontrivial $p$-torsion only if $ i = r_j +m p$ for a Hodge-Tate weight $ r_j$ of $T$ and $m$ a positive integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13422 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Torsion graded pieces of Nyggard filtration for crystalline representation Liu, Tong Number Theory Algebraic Geometry Let $K$ be a unramified $p$-adic field with the absolute Galois group $G_K$ and $T$ a crystalline $\mathbb Z_p$-representation of $G_K$. We study the graded pieces of integral filtration on $D_{\rm dR}(T)$ given by Nyggard filtration of the attached Breuil-Kisin module of $T$. We show that the $i$-graded piece has nontrivial $p$-torsion only if $ i = r_j +m p$ for a Hodge-Tate weight $ r_j$ of $T$ and $m$ a positive integer. |
| title | Torsion graded pieces of Nyggard filtration for crystalline representation |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2408.13422 |