Mazur, B. [Goldfeld, D.] Rational isogenies of prime degree. (With an appendix by D. Goldfeld). (English) Zbl 0386.14009 Invent. Math. 44, 129-162 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 28 ReviewsCited in 351 Documents MathOverflow Questions: Failure of injectiveness of maps between cotangent spaces of abelian varieties MSC: 14G05 Rational points 14H45 Special algebraic curves and curves of low genus 14H52 Elliptic curves 14L30 Group actions on varieties or schemes (quotients) 11F03 Modular and automorphic functions 14E30 Minimal model program (Mori theory, extremal rays) 14H40 Jacobians, Prym varieties PDFBibTeX XMLCite \textit{B. Mazur}, Invent. Math. 44, 129--162 (1978; Zbl 0386.14009) Full Text: DOI EuDML References: [1] Atkin, A.O.L., Lehner, J.: Hecke operators on 161-1. Math. Ann.185, 134-160 (1970) · doi:10.1007/BF01359701 [2] Artin, M.: The implicit function theorem in algebraic geometry. 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France, Mémoire43, 1-80 (1975) · Zbl 0322.14011 [15] Linnik, J.V., Vinogradov, A.I.: Hypoelliptic curves and the least prime quadratic residue. [in Russian] Dokl. Akad. Nauk CCCP168, 259-261 (1966). [Eng. transl.: Soviet Math. Dokl.7, 612-614 (1966)] · Zbl 0148.02305 [16] Manin, Y.: A uniform bound forp-torsion in elliptic curves [in Russian]. Izv. Akad. Nauk CCCP33, 459-465 (1969) · Zbl 0191.19601 [17] Manin, Y.: Parabolic points and zeta functions of modular curves [in Russian]. Izv. Akad. Nauk CCCP36, 19-65 (1972). [English transl.: Math. USSR Izv.6, 19-64 (1972)] · Zbl 0243.14008 [18] Mazur, B.: Rational points on modular curves. Proceedings of a conference on modular functions held in Bonn 1976. Lecture Notes in Math., 601, Berlin-Heidelberg-New York: Springer 1977 [19] Mazur, B.: Modular curves and the Eisenstein ideal. Publ. Math. I.H.E.S.47 (1977) · Zbl 0394.14008 [20] Mazur, B.:p-adic analytic number theory of elliptic curves and abelian varieties overQ. 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Dieudonné) II. Étude globale élémentaire de quelques classes de morphismes. Publ. Math. I.H.E.S.8 (1961). IV Étude locale des schémas et des morphismes de schémas. Publ. Math. I.H.E.S.32 (1967) [45] [SGA 7II] Groupes de Monodromie en Géométrie Algébrique (dirigé par A. Grothendieck avec la collaboration de M. Raynaud et D.S. Rim). Lecture Notes in Mathematics 288, Berlin-Heidelberg-New York: Springer 1972 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.