Euler systems obtained from congruences between Hilbert modular forms

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1. [BD1] M. BERTOLINI - H. DARMON, A rigid analytic Gross-Zagier formula and arithmetic applications. With an appendix by Bas Edixhoven. Ann. of Math. (2) 146, no. 1 (1997), pp. 111-147. Zbl1029.11027MR1469318
2. [BD2] M. BERTOLINI - H. DARMON, Iwasawa's main conjecture for elliptic curves over anticyclotomic Zp-extensions. Ann. of Math. (2) 162, no. 1 (2005), pp. 1-64. Zbl1093.11037MR2178960
3. [BLR] N. BOSTON - H. W. LENSTRA - K. A. RIBET, Quotients of group rings arising from two-dimensional representations. (English. French summary) C. R. Acad. Sci. Paris Sér. I Math., 312, no. 4 (1991), pp. 323-328 Zbl0718.16018MR1094193
4. [BC] J.-F. BOUTOT - H. CARAYOL, Uniformisation p-adique des courbes de Shimura: les théoròmes de CÏerednik et de Drinfeld. (French) [p-adic uniformization of Shimura curves: the theorems of Cherednik and Drinfeld] Courbes modulaires et courbes de Shimura (Orsay, 1987/1988). Astérisque No. 7 (1991), pp. 196-197 (1992), pp. 45-158 . Zbl0781.14010MR1141456
5. [Ca] H. CARAYOL. Sur les représentations galoisiennes modulo l attachées aux formes modulaires. (French) [On Galois representations modulo l associated with modular forms] Duke Math. J., 59, no. 3 (1989), pp. 785-801. Zbl0703.11027MR1046750
6. [Ce] I. V. CÏEREDNIK, Uniformization of algebraic curves by discrete arithmetic subgroups of PGL2(kw) with compact quotient spaces. (Russian) Mat. Sb. (N.S.) 100(142), 165, no. 1 (1976), pp. 59-88. Zbl0379.14010MR491706
7. [CG] J. COATES - R. GREENBERG, Kummer theory for abelian varieties over local fields. Invent. Math., 124, no. 1-3 (1996), pp. 129-174. Zbl0858.11032MR1369413
8. [DT] F. DIAMOND - R. TAYLOR, Nonoptimal levels of mod l modular representations. Invent. Math., 115, no. 3 (1994), pp. 435-462. Zbl0847.11025MR1262939
9. [Dr] V. G. DRINFELD, Coverings of p-adic symmetric domains. (Russian) Funkcional. Anal. i PrilozÏen., 10, no. 2 (1976), pp. 29-40. Zbl0346.14010MR422290
10. [GP] L. GERRITZEN, M. VAN DER PUT, Schottky groups and Mumford curves. Lecture Notes in Mathematics, 817. Springer, Berlin, 1980. viii+317 pp. Zbl0442.14009MR590243
11. [Go] E. GOREN, Lectures on Hilbert modular varieties and modular forms. With the assistance of Marc-Hubert Nicole. CRM Monograph Series, 14. American Mathematical Society, Providence, RI, 2002. Zbl0986.11037MR1863355
12. [Gr] B. H. GROSS, Heights and the special values of L-series. Number theory (Montreal, Que., 1985), pp. 115-187, CMS Conf. Proc., 7, Amer. Math. Soc., Providence, RI, 1987. Zbl0623.10019MR894322
13. [GZ] B. H. GROSS - D. B. ZAGIER, Heegner points and derivatives of L-series. Invent. Math., 84, no. 2 (1986), pp. 225-320. Zbl0608.14019MR833192
14. [Gt] A. GROTHENDIECK, Groupes de monodromie en géométrie algébrique. I. (French) Séminaire de Géométrie Algébrique du Bois-Marie 1967-1969 (SGA 7 I). Dirigé par A. Grothendieck. Avec la collaboration de M. Raynaud et D. S. Rim. Lecture Notes in Mathematics, Vol. 288. Springer-Verlag, Berlin-New York, 1972. viii+523 pp. Zbl0237.00013MR354656
15. [JL] H. JACQUET - R. P. LANGLANDS, Automorphic forms on GL(2). Lecture Notes in Mathematics, Vol. 114. Springer-Verlag, Berlin-New York, 1970. vii+548 pp. Zbl0236.12010MR401654
16. [J1] F. JARVIS, Correspondences on Shimura curves and Mazur's principle at p. Pacific J. Math., 213, no. 2 (2004), pp. 267-280. Zbl1073.11030MR2036920
17. [JL] JORDAN - BRUCE W. - LIVNÉ - RON A., Local Diophantine properties of Shimura curves. Math. Ann., 270, no. 2 (1985), pp. 235-248. Zbl0536.14018MR771981
18. [J2] F. JARVIS, Mazur's principle for totally real fields of odd degree. Compositio Math., 116, no. 1 (1999), pp. 39-79. Zbl1053.11043MR1669444
19. [J3] F. JARVIS, Level lowering for modular mod l representations over totally real fields. Math. Ann., 313, no. 1 (1999), pp. 141-160. Zbl0978.11020MR1666809
20. [K1] V. A. KOLYVAGIN, Finiteness of E(Q) and I–I–I(E; Q) for a subclass of Weil curves. (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 52, no. 3 (1988), pp. 522-540, 670-671; translation in Math. USSR-Izv., 32, no. 3 (1989), pp. 523-541. Zbl0662.14017MR954295
21. [K2] V. A. KOLYVAGIN, The Mordell-Weil and Shafarevich-Tate groups for Weil elliptic curves. (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 52, no. 6 (1988), pp. 1154-1180, 1327; translation in Math. USSR-Izv., 33, no. 3 (1989), pp. 473-499. Zbl0681.14016MR984214
22. [K3] V. A. KOLYVAGIN, Euler systems. The Grothendieck Festschrift, Vol. II, 435-483, Progr. Math., 87, Birkäuser Boston, Boston, MA, 1990. Zbl0742.14017MR1106906
23. [KL1] V. A. KOLYVAGIN - D. Y. LOGACHËV, Finiteness of the Shafarevich-Tate group and the group of rational points for some modular abelian varieties. (Russian) Algebra i Analiz, 1, no. 5 (1989), pp. 171-196; translation in Leningrad Math. J., 1, no. 5 (1990), pp. 1229-1253. Zbl0728.14026MR1036843
24. [KL2] V. A. KOLYVAGIN - D. Y. LOGACHËV, Finiteness of I–I–I over totally real fields. (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 55, no. 4 (1991), pp. 851-876; translation in Math. USSR-Izv., 39, no. 1 (1992), pp. 829-853. Zbl0791.14019MR1137589
25. [L1] M. LONGO, On the Birch and Swinnerton-Dyer conjecture over totally real fields. PhD thesis, Dipartimento di Matematica P. e A., Padova, 2004. 
26. [L2] M. LONGO, On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields. Ann. Inst. Fourier (Grenoble) 56, no. 3 (2006), pp. 689-733. Zbl1152.11028MR2244227
27. [L3] M. LONGO, On the anticyclotomic Iwasawa's main conjecture for Hilbert modular forms. Submitted. Zbl1306.11087
28. [Mi] J. S. MILNE, Arithmetic duality theorems. Perspectives in Mathematics, 1. Academic Press, Inc., Boston, MA, 1986. x+421 pp. Zbl0613.14019MR881804
29. [Ra] A. RAJAEI, On the levels of mod l Hilbert modular forms. J. Reine Angew. Math. 537 (2001), pp. 33-65. Zbl0982.11023MR1856257
30. [Ri] K. A. RIBET. On modular representations of Gal(Q=Q) arising from modular forms. Invent. Math., 100, no. 2 (1990), pp. 431-476. Zbl0773.11039MR1047143
31. [Ru] K. RUBIN, Euler systems. Annals of Mathematics Studies, 147. Hermann Weyl Lectures. The Institute for Advanced Study. Princeton University Press, Princeton, NJ, 2000. Zbl0977.11001MR1749177
32. [Se] J.-P. SERRE. Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. Invent. Math., 15, no. 4 (1972), pp. 259-331. Zbl0235.14012MR387283
33. [S1] G. SHIMURA, The special values of the zeta functions associated with Hilbert modular forms. Duke Math. J., 45, no. 3 (1978), pp. 637-679. Zbl0394.10015MR507462
34. [S2] G. SHIMURA, Introduction to the arithmetic theory of automorphic functions. KanÎ Memorial Lectures, No. 1. Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. xiv+267 pp. Zbl0221.10029MR314766
35. [Ta] R. TAYLOR, On Galois representations associated to Hilbert modular forms. Invent. Math., 98, no. 2 (1989), pp. 265-280. Zbl0705.11031MR1016264
36. [Va] V. VATSAL, Special value formulae for Rankin L-functions. Math. Sci. Res. Inst. Publ., 49, Cambridge Univ. Press, Cambridge, 2004. Zbl1077.11038MR2083212
37. [Vi] M.-F. VIGNÉRAS. Arithmétique des algèbres de quaternions. (French) Zbl0422.12008
38. [Arithmetic of quaternion algebras] Lecture Notes in Mathematics, 800. Springer, Berlin, 1980. vii+169 pp. MR580949
39. [Wa] J.-L. WALDSPURGER, Correspondances de Shimura et quaternions. (French) [Shimura correspondences and quaternions] Forum Math., 3, no. 3 (1991), pp. 219-307. Zbl0724.11026MR1103429
40. [Wi] A. WILES, On ordinary l-adic representations associated to modular forms. Invent. Math., 94, no. 3 (1988), pp. 529-573. Zbl0664.10013MR969243
41. [Z1] S. ZHANG, Heights of Heegner points on Shimura curves. Ann. of Math. (2) 153, no. 1 (2001), pp. 27-147. Zbl1036.11029MR1826411
42. [Z2] S. ZHANG, Gross-Zagier formula for GL2. Asian J. Math., 5, no. 2 (2001), pp. 183-290. Zbl1111.11030MR1868935