Reductions of Galois representations of Slope $\frac{3}{2}$

Eknath Ghate; Vivek Rai

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arXiv · 1901.01728

Reductions of Galois representations of Slope $\frac{3}{2}$

Eknath Ghate·Vivek Rai

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Abstract

We prove a zig-zag conjecture describing the reductions of irreducible crystalline two-dimensional representations of $G_{{\mathbb{Q}}_p}$ of slope $\frac{3}{2}$ and exceptional weights. This along with previous works completes the description of the reduction for all slopes less than $2$. The proof involves computing the reductions of the Banach spaces attached by the $p$-adic LLC to these representations, followed by an application of the mod $p$ LLC to recover the reductions of these representations.

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BibTeX RIS

Eknath Ghate, Vivek Rai. 2019-01-07. Reductions of Galois representations of Slope $\frac{3}{2}$. https://arxiv.org/abs/1901.01728

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