JP Journal of Algebra, Number Theory and Applications
Volume 20, Issue 1, Pages 109 - 119
(February 2011)
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ON PROJECTIVELY RATIONAL LIFTS OF MOD 7 GALOIS REPRESENTATIONS
Iftikhar Burhanuddin and Luis Dieulefait
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Abstract: We consider the problem of constructing ?projectively rational? lifts of odd, two-dimensional Galois representations with values in ?Using modular forms, in particular, the theory of congruences, we compute such lifts for many examples of mod 7 representations thus giving evidence that suggests that such lifts may always exist. We also consider the invariance after twist (weight change) of the existence of such lifts. |
Keywords and phrases: projectively rational, Galois representations, modularity conjecture. |
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