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Reductions of Galois representations of slope $2$
Abstract
Let p be a prime ≥ 5. We determine the semisimplifications of the mod p reductions of irreducible two-dimensional crystalline representations of the Galois group of ℚp of slope $2$ and weights k≥3p+4 with k not ≡ 6 bmod (p−1). The proof relies on the compatibility between the p-adic and the mod p Local Langlands Correspondences for GL2(ℚp).
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BibTeX
@misc{ghate2026reductions,
title = {{Reductions of Galois representations of slope $2$}},
author = {Eknath Ghate and Sudipta Majumder},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19293},
eprint = {2610.19293},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19293},
}
RIS
TY - UNPB
TI - Reductions of Galois representations of slope $2$
AU - Eknath Ghate
AU - Sudipta Majumder
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.19293
UR - https://arxiv.org/abs/2610.19293
AB - Let p be a prime ≥ 5. We determine the semisimplifications of the mod p reductions of irreducible two-dimensional crystalline representations of the Galois group of ℚ_p of slope $2$ and weights k≥3p+4 with k not ≡ 6 bmod (p−1). The proof relies on the compatibility between the p-adic and the mod p Local Langlands Correspondences for GL_2(ℚ_p).
ER -