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Constructing semisimple p-adic Galois representations with prescribed properties

Chandrashekhar Khare·Michael Larsen·Ravi Ramakrishna
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Abstract

In this paper we show that two dimensional (mod p) Galois representations satisfying mild hypotheses can be lifted to p-adic Galois representations ramified at infinitely many primes such that the characteristic polynomials of Frobenius at a density one set of unramified primes are defined over the rational integers. In particular we show that often one can "density one compatibly" lift mod p and mod q Galois representations.

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Chandrashekhar Khare, Michael Larsen, Ravi Ramakrishna. 2003-09-17. Constructing semisimple p-adic Galois representations with prescribed properties. https://arxiv.org/abs/math/0309283

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