TY - JOUR
T1 - Q-motives and modular forms
AU - Yamauchi, Takuya
N1 - Funding Information:
The author expresses sincere thanks to Y. Andre, N. Tsuzuki, K. Ribet and C. Khare for valuable comments. Especially, N. Takahashi has discussed with the author during the preparation of this paper. The author gives special thanks to him. The author is partially supported by JSPS Grant-in-Aid for Scientific Research No. 19740017 and JSPS Core-to-Core Program No. 18005.
PY - 2008/6
Y1 - 2008/6
N2 - A Q-curve is an elliptic curve E over over(Q, -) which is isogenous to all its Galois conjugates. Serre's conjecture implies that Q-curves are modular. This means that E is a over(Q, -)-simple factor of J1 (N) for some level N. In this paper we will introduce Q-motives which are generalizations of Q-curves and present basic properties of Q-motives. Their properties are proved under some standard conjectures for motives.
AB - A Q-curve is an elliptic curve E over over(Q, -) which is isogenous to all its Galois conjugates. Serre's conjecture implies that Q-curves are modular. This means that E is a over(Q, -)-simple factor of J1 (N) for some level N. In this paper we will introduce Q-motives which are generalizations of Q-curves and present basic properties of Q-motives. Their properties are proved under some standard conjectures for motives.
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U2 - 10.1016/j.jnt.2008.03.001
DO - 10.1016/j.jnt.2008.03.001
M3 - Article
AN - SCOPUS:43049084090
SN - 0022-314X
VL - 128
SP - 1485
EP - 1505
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 6
ER -