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

Shalini Bhattacharya; Eknath Ghate

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

Number Theory 2015-04-02 v1

Authors: Shalini Bhattacharya , Eknath Ghate

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 $GL_2(F_p)$ .

Keywords

Galois representation mod p reduction slope crystalline representation Local Langlands Correspondence symmetric power semisimplification

Cite

@article{arxiv.1504.00148,
  title  = {Reductions of Galois representations for slopes in $(1,2)$},
  author = {Shalini Bhattacharya and Eknath Ghate},
  journal= {arXiv preprint arXiv:1504.00148},
  year   = {2015}
}

Comments

41 pages

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