TY - JOUR
T1 - On the modularity of Q-curves
AU - Ellenberg, Jordan S.
AU - Skinner, Chris
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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.
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U2 - 10.1215/S0012-7094-01-10914-9
DO - 10.1215/S0012-7094-01-10914-9
M3 - Article
AN - SCOPUS:0012957774
SN - 0012-7094
VL - 109
SP - 97
EP - 122
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 1
ER -