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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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 709-734
Launched on MUSE
2005-07-29
Open Access
No
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