Reductions of Galois representations of Slope (3)/(2)

2019/01/07 by Ghate, Eknath, Rai, Vivek · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1901.01728

Abstract

We prove a zig-zag conjecture describing the reductions of irreducible crystalline two-dimensional representations of G_ℚp of slope (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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