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
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