Galois actions on Q-curves and winding quotients

Francesc Bars, Luis Dieulefait

Research output: Contribution to journalArticleResearchpeer-review

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.
Original languageEnglish
Pages (from-to)531-538
JournalMathematische Zeitschrift
Volume254
Issue number3
DOIs
Publication statusPublished - 1 Nov 2006

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