Reductions of Galois representations for slopes in $(1,2)$

Shalini Bhattacharya; Eknath Ghate

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arXiv · 1504.00148

Reductions of Galois representations for slopes in $(1,2)$

Shalini Bhattacharya·Eknath Ghate

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Abstract

We describe the semi-simplification of the mod $p$ reduction of certain crystalline two dimensional local Galois representations of slopes in the interval $(1,2)$ and all weights. The proof uses the mod $p$ Local Langlands Correspondence for $GL_2(Q_p)$. We also give a complete description of the submodules generated by the second highest monomial in the mod $p$ symmetric power representations of $GL_2(F_p)$.

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Shalini Bhattacharya, Eknath Ghate. 2015-04-01. Reductions of Galois representations for slopes in $(1,2)$. https://arxiv.org/abs/1504.00148

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