In mathematics, the Shimura subgroup Σ(N) is a subgroup of the Jacobian of the modular curveX0(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.
ReferencesEdit
Ling, San; Oesterlé, Joseph (1991), "The Shimura subgroup of J0(N)", Astérisque (196): 171–203, ISSN 0303-1179, MR 1141458
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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shimura, subgroup, mathematics, subgroup, jacobian, modular, curve, level, given, kernel, natural, jacobian, named, after, goro, shimura, there, similar, subgroup, associated, shimura, curves, quaternion, algebras, references, editling, oesterlé, joseph, 1991,. In mathematics the Shimura subgroup S 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 S N D associated to Shimura curves of quaternion algebras References EditLing San Oesterle Joseph 1991 The Shimura subgroup of J0 N Asterisque 196 171 203 ISSN 0303 1179 MR 1141458 Mazur Barry 1977 Modular curves and the Eisenstein ideal Publications Mathematiques de l IHES 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 Seminaire de Theorie des Nombres 1987 1988 Talence 1987 1988 Talence Univ Bordeaux I pp Exp No 6 10 MR 0993107 nbsp This number theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Shimura subgroup amp oldid 1043620996, wikipedia, wiki, book, books, library,
