Stark-Heegner points on modular jacobians
Dasgupta, Samit
Annales scientifiques de l'École Normale Supérieure, Tome 38 (2005), p. 427-469 / Harvested from Numdam
@article{ASENS_2005_4_38_3_427_0,
     author = {Dasgupta, Samit},
     title = {Stark-Heegner points on modular jacobians},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {38},
     year = {2005},
     pages = {427-469},
     doi = {10.1016/j.ansens.2005.03.002},
     zbl = {02213129},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2005_4_38_3_427_0}
}
Dasgupta, Samit. Stark-Heegner points on modular jacobians. Annales scientifiques de l'École Normale Supérieure, Tome 38 (2005) pp. 427-469. doi : 10.1016/j.ansens.2005.03.002. http://gdmltest.u-ga.fr/item/ASENS_2005_4_38_3_427_0/

[1] Bertolini M., Darmon H., Heegner points, p-adic L-functions and the Cerednik-Drinfeld uniformization, Invent. Math. 131 (1998) 453-491. | MR 1614543 | Zbl 0899.11029

[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 1133878 | Zbl 0761.14015

[5] Bosch S., Lútkebohmert W., Raynaud M., Néron Models, Ergeb. Math. Grenzgeb. (3), vol. 21, Springer, Berlin, 1990. | MR 1045822 | Zbl 0705.14001

[6] Darmon H., Integration on H p ×H and arithmetic applications, Ann. of Math. (2) 154 (3) (2001) 589-639. | MR 1884617 | Zbl 1035.11027

[7] Darmon H., Dasgupta S., Elliptic units for real quadratic fields, Ann. of Math., submitted for publication. | Zbl 05050054

[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 1960299 | Zbl 1040.11048

[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 337993 | Zbl 0281.14010

[13] De Shalit E., p-adic periods and modular symbols of elliptic curves of prime conductor, Invent. Math. 121 (2) (1995) 225-255. | MR 1346205 | Zbl 1044.11576

[14] De Shalit E., On the p-adic periods of X 0 p, Math. Ann. 303 (1995) 457-472. | MR 1355000 | Zbl 0864.14014

[15] Gerritzen L., Van Der Put M., Schottky Groups and Mumford Curves, Lecture Notes in Math., vol. 817, Springer, Berlin, 1980. | MR 590243 | Zbl 0442.14009

[16] Greenberg R., Stevens G., p-adic L-functions and p-adic periods of modular forms, Invent. Math. 111 (2) (1993) 407-447. | MR 1198816 | Zbl 0778.11034

[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 1279610 | Zbl 0846.11030

[18] Griffiths P., Harris J., Principles of Algebraic Geometry, Reprint of the 1978 original, Wiley Classics Library, Wiley, New York, 1994. | MR 1288523 | Zbl 0836.14001

[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 656068 | Zbl 0507.12010

[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 1110395 | Zbl 0743.14021

[21] Gross B.H., Zagier D.B., Heegner points and derivatives of L-series, Invent. Math. 84 (2) (1986) 225-320. | MR 833192 | Zbl 0608.14019

[22] Hida H., Iwasawa modules attached to congruences of cusp forms, Ann. Sci. École Norm. Sup. (4) 19 (2) (1986) 231-273. | Numdam | MR 868300 | Zbl 0607.10022

[23] Ichikawa T., Schottky uniformization theory on Riemann surfaces Mumford curves of infinite genus, J. reine Angew. Math. 486 (1997) 45-68. | MR 1450750 | Zbl 0872.14020

[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 289518 | Zbl 0228.14009

[25] Koebe P., Über die Uniformisierung der algebraischen Kurven IV, Math. Ann. 75 (1914) 42-129. | JFM 45.0669.01 | MR 1511787

[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 1106906 | Zbl 0742.14017

[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 1036843 | Zbl 0728.14026

[28] Manin J.I., Parabolic points and zeta functions of modular curves, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1) (1972) 19-66. | MR 314846 | Zbl 0243.14008

[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 396582 | Zbl 0275.14017

[30] Mazur B., Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. 47 (1977) 33-186, (1978). | Numdam | MR 488287 | Zbl 0394.14008

[31] Mazur B., On the arithmetic of special values of L functions, Invent. Math. 55 (3) (1979) 207-240. | MR 553997 | Zbl 0426.14009

[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 830037 | Zbl 0699.14028

[33] Mazur B., Wiles A., Class fields of Abelian extensions of Q, Invent. Math. 76 (2) (1984) 179-330. | MR 742853 | Zbl 0545.12005

[34] Mazur B., Wiles A., On p-adic analytic families of Galois representations, Compositio Math. 59 (2) (1986) 231-264. | Numdam | MR 860140 | Zbl 0654.12008

[35] Mumford D., An analytic construction of degenerating curves over complete local rings, Compositio Math. 24 (2) (1972) 129-174. | Numdam | MR 352105 | Zbl 0228.14011

[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 804706 | Zbl 0575.10024

[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 19.0424.02

[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 607504 | Zbl 1013.20001

[39] Teitelbaum J., p-adic periods of genus two Mumford-Schottky curves, J. reine Angew. Math. 385 (1988) 117-151. | MR 931217 | Zbl 0636.14011

[40] Washington L., Galois cohomology, in: Modular Forms and Fermat's Last Theorem, Boston, MA, 1995, Springer, New York, 1997, pp. 101-120. | MR 1638477 | Zbl 0928.12003