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

2015/04/01 by Shalini Bhattacharya, Eknath Ghate, Bhattacharya, Shalini +1 · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Primary: 11F80 #math.NT #msc:11F80

paper · pdf · doi:10.48550/arxiv.1504.00148

41 pages

arxiv created 2015/04/01 · arxiv updated 2015/04/02

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 GL₂(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 GL₂(F_p).

Cited by

• The semi-stable Local Langlands Correspondence

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• Reductions of modular Galois representations of Slope (2,3)