Endomorphism algebras of motives attached to elliptic modular forms
Alexander F. Brown[1]; Eknath P. Ghate[1]
- [1] Tata Institute of Fundamental Research, School of Mathematics, Homi Bhabha Road, Mumbai 400 005 (India)
Annales de l’institut Fourier (2003)
- Volume: 53, Issue: 6, page 1615-1676
- ISSN: 0373-0956
Access Full Article
topAbstract
topHow to cite
topReferences
top- A.O.L. Atkin, Wen Ch'ing Winnie Li, Twists of newforms and pseudo-eigenvalues of W-operators, Invent. Math. 48 (1978), 221-243 Zbl0369.10016MR508986
- D. Blasius, J. Rogawski., Motives for Hilbert modular forms, Invent. Math. 114 (1993), 55-87 Zbl0829.11028MR1235020
- C. Breuil, Lectures on p-adic Hodge theory, deformations and local Langlands, Advanced Course Lecture Notes 20, Centre de Recerca Matemàtica, Barcelona
- P. Deligne, Formes modulaires et représentations -adiques, Séminaire Bourbaki, 1968/1969 179, exp. 355 (1971), 139-172, Springer-Verlag Zbl0206.49901
- P. Deligne, M. Rapoport, Les schémas de modules de courbes elliptique, Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Vol. 349 (1973), 143-316 Zbl0281.14010
- M. Demazure, Lectures on p-divisible groups, 302 (1972), Springer-Verlag Zbl0247.14010MR344261
- G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpen, Invent. Math. 73 (1983), 349-366 Zbl0588.14026MR718935
- J.-M. Fontaine, B. Mazur, Geometric Galois representations, 1 (1995), International Press Zbl0839.14011MR1363495
- H. Hida, Modular Forms and Galois Cohomology, (2000), Cambridge University Press, Cambridge Zbl0952.11014MR1779182
- U. Jannsen, Motives, numerical equivalence, and semi-simplicity, Invent. Math. 107 (1992), 447-452 Zbl0762.14003MR1150598
- F. Momose, On the -adic representations attached to modular forms, J. Fac. Sci. Univ. Tokyo, Sect. IA Math. 28 (1981), 89-109 Zbl0482.10023MR617867
- J. Quer, La classe de Brauer de l'algèbre d'endomorphismes d'une variété abélienne modulaire, C. R. Acad. Sci. Paris, Sér. I Math. 327 (1998), 227-230 Zbl0936.14032MR1650241
- K. Ribet, Twists of modular forms and endomorphisms of abelian varieties, Math. Ann. 253 (1980), 43-62 Zbl0421.14008MR594532
- K. Ribet, Endomorphism algebras of abelian varieties attached to newforms of weight 2, Seminar on Number Theory, Paris 1979-1980 12 (1981), 263-276, Birkhäuser, Boston, Mass. Zbl0467.14006
- K. Ribet, Abelian varieties over and modular forms, Proc. KAIST Math. Workshop (1992), 53-79
- A. Scholl, Motives for modular forms, Invent. Math. 100 (1990), 419-430 Zbl0760.14002MR1047142
- J.-P. Serre, Quelques applications du théorème de densité de Chebotarev, Publ. Math. Inst. Hautes Études Sci. 54 (1981), 323-401 Zbl0496.12011MR644559
- G. Shimura, On elliptic curves with complex multiplication as factors of the Jacobians of modular function fields, Nagoya Math. J. 43 (1971), 199-208 Zbl0225.14015MR296050
- G. Shimura, On the factors of the Jacobian variety of a modular function field, J. Math. Soc. Japan 25 (1973), 523-544 Zbl0266.14017MR318162
- W. Stein, The first newform such that for all , (2000)
- M. Volkov, Les représentations -adiques associées aux courbes elliptiques sur , J. reine angew. Math. 535 (2001), 65-101 Zbl1024.11038MR1837096