Galois actions on Q-curves and winding quotients |
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Authors: | Francesc Bars Luis Dieulefait |
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Institution: | (1) Depart. Matemàtiques, Fac. Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia, Spain;(2) Depart. d'Algebra i Geometria, Facultat Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain |
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Abstract: | We prove two ``large images' results for the Galois representations attached to a degree d Q-curve E over a quadratic field K: if K is arbitrary, we prove maximality of the image for every prime p>13 not dividing d, provided that d is divisible by q (but d≠q) with q=2 or 3 or 5 or 7 or 13. If K is real we prove maximality of the image for every odd prime p not dividing d
D, where D= disc(K), provided that E is a semistable Q-curve. In both cases we make the (standard) assumptions that E does not have potentially good reduction at all primes p∤6 and that d is square free.
The first author is supported by BFM2003-06092. |
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Keywords: | 11F80 11G05 11G18 |
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