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Constructing Semisimple p-Adic Galois Representations with Prescribed Properties

Chandrashekhar Khare, Michael Larsen and Ravi Ramakrishna
American Journal of Mathematics
Vol. 127, No. 4 (Aug., 2005), pp. 709-734
Stable URL: http://www.jstor.org/stable/40067979
Page Count: 26
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Constructing Semisimple p-Adic Galois Representations with Prescribed Properties
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Abstract

Consider a characteristic p representation of the absolute Galois group of the rational numbers. In this paper we show how to deform this representation to the p-adics while guaranteeing that the characteristic polynomials of Frobenius at a density one set of primes are algebraic and pure of specified weight. The resulting representation is ramified at an infinite (density zero) set of primes. As a consequence of the technique of proof we show that one can compatibly lift a mod pq representation. Again, the resulting representation is ramified at infinitely many primes.

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