- Source: Shimura subgroup
In mathematics, the Shimura subgroup Σ(N) is a subgroup of the Jacobian of the modular curve X0(N) of level N, given by the kernel of the natural map to the Jacobian of X1(N). It is named after Goro Shimura. There is a similar subgroup Σ(N,D) associated to Shimura curves of quaternion algebras.
References
Ling, San; Oesterlé, Joseph (1991), "The Shimura subgroup of J0(N)", Astérisque (196): 171–203, ISSN 0303-1179, MR 1141458
Mazur, Barry (1977), "Modular curves and the Eisenstein ideal", Publications Mathématiques de l'IHÉS (47): 33–186, ISSN 1618-1913, MR 0488287
Ribet, Kenneth A. (1984), "Congruence relations between modular forms", Proceedings of the International Congress of Mathematicians, Vol. 1 (Warsaw, 1983), Warszawa: PWN, pp. 503–514, MR 0804706
Ribet, Kenneth A. (1988), "On the component groups and the Shimura subgroup of J0(N)", Séminaire de Théorie des Nombres, 1987--1988 (Talence, 1987--1988), Talence: Univ. Bordeaux I, pp. Exp. No. 6, 10, MR 0993107
Kata Kunci Pencarian:
- Shimura subgroup
- Goro Shimura
- Shimura variety
- Congruence subgroup
- Eichler–Shimura isomorphism
- Hyperspecial subgroup
- Wiles's proof of Fermat's Last Theorem
- Arithmetic group
- CM-field
- Modular curve
