Behaviour of Certain Crystalline Representations modulo $2$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909013641265152 |
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| author | Bhattacharya, Shalini Venugopal, Arathy |
| author_facet | Bhattacharya, Shalini Venugopal, Arathy |
| contents | We compute the explicit form of the semisimplified reduction modulo $2$ of the $2$-adic crystalline Galois representations $V_{k,a_2}$ at small slopes in $(0,1]$, using the compatibility of $2$-adic and mod-$2$ local Langlands correspondence. We find parameters $α'(k,a_{2})$ and $α(k,a_{2})$, which play a crucial role in determining the reduction of $V_{k,a_{2}}$ for slopes in the range $(0,1)$ and slope $1$ respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03424 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Behaviour of Certain Crystalline Representations modulo $2$ Bhattacharya, Shalini Venugopal, Arathy Number Theory 11F80 We compute the explicit form of the semisimplified reduction modulo $2$ of the $2$-adic crystalline Galois representations $V_{k,a_2}$ at small slopes in $(0,1]$, using the compatibility of $2$-adic and mod-$2$ local Langlands correspondence. We find parameters $α'(k,a_{2})$ and $α(k,a_{2})$, which play a crucial role in determining the reduction of $V_{k,a_{2}}$ for slopes in the range $(0,1)$ and slope $1$ respectively. |
| title | Behaviour of Certain Crystalline Representations modulo $2$ |
| topic | Number Theory 11F80 |
| url | https://arxiv.org/abs/2605.03424 |