Stark-Heegner points on modular jacobians

Dasgupta, Samit

doi:10.1016/j.ansens.2005.03.002

Dasgupta, Samit

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 3, pp. 427-469.

Zbl

DOI : 10.1016/j.ansens.2005.03.002

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     author = {Dasgupta, Samit},
     title = {Stark-Heegner points on modular jacobians},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {427--469},
     publisher = {Elsevier},
     volume = {Ser. 4, 38},
     number = {3},
     year = {2005},
     doi = {10.1016/j.ansens.2005.03.002},
     zbl = {02213129},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.ansens.2005.03.002/}
}

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Dasgupta, Samit. Stark-Heegner points on modular jacobians. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 3, pp. 427-469. doi : 10.1016/j.ansens.2005.03.002. http://www.numdam.org/articles/10.1016/j.ansens.2005.03.002/

Bibliographie
Cité par

[1] Bertolini M., Darmon H., Heegner points, p-adic L-functions and the Cerednik-Drinfeld uniformization, Invent. Math. 131 (1998) 453-491. | MR | Zbl

[2] Bertolini M., Darmon H., The rationality of Stark-Heegner points over genus fields of real quadratic fields, in preparation.

[3] Bertolini M., Darmon H., Dasgupta S., Stark-Heegner points and special values of L-series, in preparation.

[4] Bosch S., Lütkebohmert W., Degenerating Abelian varieties, Topology 30 (4) (1991) 653-698. | MR | Zbl

[5] Bosch S., Lútkebohmert W., Raynaud M., Néron Models, Ergeb. Math. Grenzgeb. (3), vol. 21, Springer, Berlin, 1990. | MR | Zbl

[6] Darmon H., Integration on $H_{p} \times H$ and arithmetic applications, Ann. of Math. (2) 154 (3) (2001) 589-639. | MR | Zbl

[7] Darmon H., Dasgupta S., Elliptic units for real quadratic fields, Ann. of Math., submitted for publication. | Zbl

[8] Darmon H., Green P., Elliptic curves and class fields of real quadratic fields: Algorithms and verifications, Experimental Math. 11 (1) (2002) 37-55. | MR | Zbl

[9] Darmon H., Pollack R., The efficient calculation of Stark-Heegner points via overconvergent modular symbols, in preparation.

[10] Dasgupta S., Gross-Stark units, Stark-Heegner points, and class fields of real quadratic fields, PhD thesis, University of California-Berkeley, May 2004.

[11] Dasgupta S., Computations of elliptic units for real quadratic fields, Canad. J. Math., in press.

[12] Deligne P., Rapoport M., Les schémas de modules de courbes elliptiques, in: Modular Functions of One Variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Lecture Notes in Math., vol. 349, Springer, Berlin, 1973, pp. 143-316. | MR | Zbl

[13] De Shalit E., p-adic periods and modular symbols of elliptic curves of prime conductor, Invent. Math. 121 (2) (1995) 225-255. | MR | Zbl

[14] De Shalit E., On the p-adic periods of $X_{0} (p)$ , Math. Ann. 303 (1995) 457-472. | MR | Zbl

[15] Gerritzen L., Van Der Put M., Schottky Groups and Mumford Curves, Lecture Notes in Math., vol. 817, Springer, Berlin, 1980. | MR | Zbl

[16] Greenberg R., Stevens G., p-adic L-functions and p-adic periods of modular forms, Invent. Math. 111 (2) (1993) 407-447. | MR | Zbl

[17] Greenberg R., Stevens G., On the conjecture of Mazur, Tate, and Teitelbaum, in: p-Adic Monodromy and the Birch and Swinnerton-Dyer conjecture, Boston, MA, 1991, Contemp. Math., vol. 165, American Mathematical Society, Providence, RI, 1994, pp. 123-211. | MR | Zbl

[18] Griffiths P., Harris J., Principles of Algebraic Geometry, Reprint of the 1978 original, Wiley Classics Library, Wiley, New York, 1994. | MR | Zbl

[19] Gross B.H., p-adic L-series at $s = 0$ , J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (3) (1981) 979-994, (1982). | MR | Zbl

[20] Gross B.H., Kolyvagin's work on modular elliptic curves, in: L-Functions and Arithmetic, Durham, 1989, London Math. Soc. Lecture Note Ser., vol. 153, Cambridge University Press, Cambridge, 1991, pp. 235-256. | MR | Zbl

[21] Gross B.H., Zagier D.B., Heegner points and derivatives of L-series, Invent. Math. 84 (2) (1986) 225-320. | MR | Zbl

[22] Hida H., Iwasawa modules attached to congruences of cusp forms, Ann. Sci. École Norm. Sup. (4) 19 (2) (1986) 231-273. | Numdam | MR | Zbl

[23] Ichikawa T., Schottky uniformization theory on Riemann surfaces Mumford curves of infinite genus, J. reine Angew. Math. 486 (1997) 45-68. | MR | Zbl

[24] Ihara Y., On Congruence Monodromy Problems, vols. 1 and 2, Lecture Notes, vols. 1-2, Department of Mathematics, University of Tokyo, Tokyo, 1968. | MR | Zbl

[25] Koebe P., Über die Uniformisierung der algebraischen Kurven IV, Math. Ann. 75 (1914) 42-129. | JFM | MR

[26] Kolyvagin V.A., Euler systems, in: The Grothendieck Festschrift, vol. II, Progr. Math., vol. 87, Birkhäuser Boston, Boston, MA, 1990, pp. 435-483. | MR | Zbl

[27] Kolyvagin V.A., Logachëv D.Y., Finiteness of the Shafarevich-Tate group and the group of rational points for some modular Abelian varieties, Algebra i Analiz 1 (5) (1989) 171-196, (in Russian); translation in, Leningrad Math. J. 1 (5) (1990) 1229-1253. | MR | Zbl

[28] Manin J.I., Parabolic points and zeta functions of modular curves, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1) (1972) 19-66. | MR | Zbl

[29] Manin Y.I., Drinfeld V., Periods of p-adic Schottky groups, Collection of articles dedicated to Helmut Hasse on his seventy-fifth birthday, J. reine Angew. Math. 262/263 (1973) 239-247. | MR | Zbl

[30] Mazur B., Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 33-186, (1978). | Numdam | MR | Zbl

[31] Mazur B., On the arithmetic of special values of L functions, Invent. Math. 55 (3) (1979) 207-240. | MR | Zbl

[32] Mazur B., Tate J., Teitelbaum J., On p-adic analogues of the conjectures of Birch-Swinnerton-Dyer, Invent. Math. 84 (1) (1986) 1-48. | MR | Zbl

[33] Mazur B., Wiles A., Class fields of Abelian extensions of Q, Invent. Math. 76 (2) (1984) 179-330. | MR | Zbl

[34] Mazur B., Wiles A., On p-adic analytic families of Galois representations, Compositio Math. 59 (2) (1986) 231-264. | Numdam | MR | Zbl

[35] Mumford D., An analytic construction of degenerating curves over complete local rings, Compositio Math. 24 (2) (1972) 129-174. | Numdam | MR | Zbl

[36] Ribet K., Congruence relations between modular forms, in: Proceedings of the International Congress of Mathematicians, vols. 1 and 2, Warsaw, 1983, PWN, Warsaw, 1984, pp. 503-514. | MR | Zbl

[37] Schottky F., Über eine specielle Function, welche bei einer bestimmten linearen Transformation ihres Arguments univerändert bleibt, J. reine Angew. Math. 101 (1887) 227-272. | JFM

[38] Serre J.-P., Trees, Translated from the French original by John Stillwell. Corrected 2nd printing of the 1980 English translation, Springer Monographs in Mathematics, Springer, Berlin, 2003. | MR | Zbl

[39] Teitelbaum J., p-adic periods of genus two Mumford-Schottky curves, J. reine Angew. Math. 385 (1988) 117-151. | MR | Zbl

[40] Washington L., Galois cohomology, in: Modular Forms and Fermat's Last Theorem, Boston, MA, 1995, Springer, New York, 1997, pp. 101-120. | MR | Zbl

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