Deformations of Galois representations and exceptional monodromy, II: raising the level

Stefan Patrikis

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arXiv · 1604.05822

Deformations of Galois representations and exceptional monodromy, II: raising the level

Stefan Patrikis

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Abstract

Building on lifting results of Ramakrishna, Khare and Ramakrishna proved a purely Galois-theoretic level-raising theorem for two-dimensional odd representations of the Galois group of Q. In this paper, we generalize these techniques from type A1 to general (semi-)simple groups. We then strengthen our previous results on constructing geometric Galois representations with exceptional monodromy groups, achieving such constructions for almost all l, rather than a density-one set, and achieving greater flexibility in the Hodge numbers of the lifts; the latter improvement requires the new level-raising result.

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Stefan Patrikis. 2016-04-21. Deformations of Galois representations and exceptional monodromy, II: raising the level. https://arxiv.org/abs/1604.05822

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