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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.03424 |
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Table of 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.