\bibitem[BC]{boutot-carayol} J-F. Boutot, H. Carayol, {\em Uniformisation $p$-adique des courbes de Shimura: les th\'eor\`emes de Cerednik et de Drinfeld}, Ast\'erisque 196-197 (1991) pp.\ 45-158. \bibitem[BD0]{bd_derived_regulators} M. Bertolini, H. Darmon, {\em Derived heights and generalized Mazur-Tate regulators} Duke Math. J. {\bf 76} (1994), no. 1, 75--111. \bibitem[BD$\frac{1}{2}$]{bd_derived_heights} M. Bertolini, H. Darmon, {\em Derived $p$-adic heights}. Amer. J. Math. {\bf 117} (1995), no. 6, 1517--1554. \bibitem[BD1]{BD1} M. Bertolini and H. Darmon, {\em Heegner points on Mumford-Tate curves}. Invent.\ Math.\ {\bf 126} (1996) 413--456. \bibitem[BD2]{BD2} M.\ Bertolini and H.\ Darmon, {\em A rigid-analytic Gross-Zagier formula and arithmetic applications}. Annals of Math.\ {\bf 146} (1997) 111-147. \bibitem[BD3]{BD3} M.\ Bertolini and H.\ Darmon, {\em Heegner points, $p$-adic $L$-functions, and the Cerednik-Drinfeld uniformization}. Invent.\ Math.\ {\bf 131} (1998), no.\ 3, 453--491. \bibitem[BD4]{BD4} M.\ Bertolini and H.\ Darmon, {\em $p$-adic periods, $p$-adic $L$-functions and the $p$-adic uniformization of Shimura curves}, Duke Math.\ J.\ {\bf 98} (1999), no.\ 2, 305--334. \bibitem[BD5]{BD5} M.~Bertolini and H.~Darmon, {\em Euler systems and Jochnowitz congruences}, Amer.\ J.\ Math.\ {\bf 121}, n.\ 2 (1999) 259-281. \bibitem[BLR]{bosch} S.\ Bosch, W.\ L\"utkebohmert, and M.\ Raynaud, N\'eron Models, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3 Folge - Band 21, Springer-Verlag, 1990. \bibitem[BoLeRi]{BLR} N.~Boston, H.~Lenstra, K.~Ribet, {\em Quotients of groups rings arising form two-dimensional representations,} C.\ R.\ Acad.\ Sci.\ Paris {\bf 312}, S\'erie I (1991) 323--328. \bibitem[Bu]{buzzard} K.\ Buzzard, {\em Integral models of certain Shimura curves,} Duke Math.\ J.\ {\bf 87}, no.\ 3 (1998), 591--612. \bibitem[Co]{cornut} C.\ Cornut, {\em R\'eduction de familles de points CM,} PhD Thesis, Universit\'e Louis Pasteur, Strasbourg, 2000. \bibitem[Dag]{daghigh} H.~Daghigh, {\em Modular forms, quaternion algebras, and special values of $L$-functions}, McGill University PhD thesis, 1997. \bibitem[Da]{darmon_thesis} H.~Darmon, {\em A refined conjecture of Mazur-Tate type for Heegner points}. Invent. Math. {\bf 110} (1992), no. 1, 123--146. \bibitem[DDT]{ddt} H.~Darmon, F.~Diamond, and R.~Taylor, {\em Fermat's Last Theorem}, Current Developments in Mathematics Vol. {\bf 1}, International Press, 1995, pp.~1--154. \bibitem[DR]{deligne-rapoport} P.\ Deligne and M.\ Rapoport, {\em Les sch\'emas de modules des courbes elliptiques,} LNM {\bf 349}, Springer-Verlag, New York, 1973, 143-316. \bibitem[Dr]{drinfeld} V.G.\ Drinfeld, {\em Coverings of $p$-adic symmetric regions}, (in Russian), Funkts.\ Anal.\ Prilozn.\ 10, 29-40, 1976. Transl.\ in Funct.\ Anal.\ Appl.\ 10, 107-115, 1976. \bibitem[DT]{diamond_taylor} Diamond, Fred; Taylor, Richard. {\em Nonoptimal levels of mod $\ell$ modular representations}. Invent. Math. {\bf 115} (1994), no. 3, 435-462. \bibitem[Ed]{bas.appendix} B.\ Edixhoven, Appendix in [BD2]. \bibitem[Ei]{eichler} M.~Eichler, {\em The basis problem for modular forms and the traces of the Hecke operators.} Modular functions of one variable, I (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), pp. 75--151. Lecture Notes in Math., Vol. 320, Springer, Berlin, 1973. \bibitem[Gr1]{gross_montreal} B.H.~Gross, {\em Heights and the special values of $L$-series}. Number theory (Montreal, Que., 1985), 115--187, CMS Conf. Proc., 7, Amer. Math. Soc., Providence, RI, 1987. \bibitem[Gr2]{gross_zagier} B.H.~Gross, D.B.~Zagier, {\em Heegner points and derivatives of $L$-series}. Invent. Math. {\bf 84} (1986), no. 2, 225--320. \bibitem[Groth]{grothendieck} A.~Grothendieck, {\em Groupes de Mo\-no\-dro\-mie en G\'eom\-\'e\-trie Al\-g\'e\-bri\-que,} SGA VII, LNM {\bf 288}, Springer-Verlag, New York, 1972. \bibitem[GvdP]{gerritzen_vdp} L. Gerritzen, M.~van der Put, Schottky Groups and Mumford Curves, Springer Lecture Notes {\bf 817}, 1980. \bibitem[I1]{ihara1} Y.\ Ihara, {\em On congruence monodromy problems,} Lect.\ Notes Univ.\ Tokyo {\bf 1} (1968). \bibitem[I2]{ihara2} Y.\ Ihara, {\em Shimura curves over finite fields and their rational points,} Contemporary Math.\ {\bf 245} (1999) 15-23. \bibitem[JoLi1]{joli.mathann} B.W.\ Jordan, R.\ Livn\'e, {\em Local diophantine properties of Shimura curves,} Math.\ Ann.\ {\bf 270} (1985) 235-248. \bibitem[JoLi2]{joli.compositio} B.W.\ Jordan, R.\ Livn\'e, {\em On the N\'eron mdel of Jacobians of Shimura curves,} Compositio Math.\ {\bf 60} (1986) 227-236. \bibitem[JoLi3]{joli.duke} B.W.\ Jordan, R.\ Livn\'e, {\em Integral Hodge theory and congruences between modular forms,} Duke Math.\ J.\ {\bf 80} (1995) 419-484. \bibitem[KM]{katz-mazur} N.\ Katz and B.\ Mazur, {\em Arithmetic moduli of elliptic curves,} Annals of Math.\ Studies 108, Princeton University Press, Princeton, NJ (USA), 1985. \bibitem[M]{manin} Y.I.~Manin, {\em p-adic automorphic functions}, J.~Soviet Math.~ {\bf 5} (1976) 279--333. \bibitem[Ma1]{mazur_special} B.~Mazur, {\em On the arithmetic of special values of $L$ functions}, Invent. Math.{\bf 55} (1979), no. 3, 207--240. \bibitem[MR]{mazur_rubin} B.~Mazur and K.~Rubin, {\em Kolyvagin systems}, preprint. \bibitem[MTT]{mtt} B.~Mazur, J.~Tate, J.~Teitelbaum, {\em On $p$-adic analogues of the conjectures of Birch and Swinnerton-Dyer}. Invent. Math. {\bf 84} (1986), no. 1, 1--48. \bibitem[Ram]{ramakrishna} R.~Ramakrishna, {\em Lifting Galois representations}. Invent. Math. {\bf 138} (1999), no. 3, 537--562. \bibitem[Ray]{raynaud.picard} M.\ Raynaud, {\em Sp\'ecialization du foncteur de Picard,} Publ.\ Math., Inst.\ Hautes Etud.\ Sc.\ {\bf 38} (1970) 27-76. \bibitem[Ri1]{ribet1} K.\ Ribet, {\em Bimodules and abelian surfaces,} Adv.\ Stud.\ Pure Math.\ {\bf 17} (1989) 359-407. \bibitem[Ri2]{ribet} K.\ Ribet, {\em On modular representation of $\Gal(\bar\Q/\Q)$ arising from modular forms,} Invent.\ Math. {\bf 100} (1990) 431-476. \bibitem[Ro]{roberts} D.\ Roberts, Shimura curves analogous to $X_0(N)$, Harvard PhD.\ Thesis, 1989. \bibitem[Ru]{rubin} K.~Rubin, Euler Systems. Annals of Mathematics Studies {\bf 147}, 227+xi pp., Princeton: Princeton University Press. \bibitem[S]{serre} J-P.~Serre, Abelian $\ell$-Adic Representations and Elliptic Curves, Addison-Wesley, 1989. \bibitem[Sh]{shimura_book} G.~Shimura, Introduction to the arithmetic theory of automorphic functions. Reprint of the 1971 original. Publications of the Mathematical Society of Japan, 11. Kan{\^o} Memorial Lectures, 1. Princeton University Press, Princeton, NJ, 1994. \bibitem[Va1]{vatsal1} V.~Vatsal, {\em Uniform distribution of Heegner points,} Invent. Math. {\bf 148}, (2002) 1--48. \bibitem[Va2]{vatsal2} V.~Vatsal, {\em Special values of anticyclotomic $L$-functions,} Duke Math Journal, to appear. \bibitem[Vi]{vigneras} M-F.\ M-F. Vigneras, {\em Arithm\'etique des alg\`ebres des quaternions,} LNM 800, Springer. \bibitem[Wa]{waterhouse} W.~ Waterhouse, {\em Abelian varieties over finite fields,} Ann.\ Sci.\ Ec.\ Nor.\ Sup., S\'erie {\bf 4} (1969) 521-560. \bibitem[W]{wiles} A.\ Wiles, {\em Modular elliptic curves and Fermat's Last Theorem,} Ann.\ Math. {\bf 141} (1995) 443-551. \bibitem[Zh]{zhang} S.~Zhang, {\em Gross-Zagier formula for $GL_2$}, manuscript, to appear.