On the modularity of Q-curves

Jordan S. Ellenberg, Chris Skinner

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

A Q-curve is an elliptic curve over a number field K which is geometrically isogenous to each of its Galois conjugates. K. Ribet [17] asked whether every Q-curve is modular, and he showed that a positive answer would follow from J.-P. Serre's conjecture on mod p Galois representations. We answer Ribet's question in the affirmative, subject to certain local conditions at 3.

Original languageEnglish (US)
Pages (from-to)97-122
Number of pages26
JournalDuke Mathematical Journal
Volume109
Issue number1
DOIs
StatePublished - Jan 1 2001

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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