Periods and points attached to quadratic algebras Massimo Bertolini Henri Darmon Peter Green September 5, 2007 Contents 1 Classical Heegner points 4 2 Heegner points and p-adic integration 9 3 Forms on T p ×H 23 4 Complex periods and Heegner points 27 5 p-adic periods and Stark-Heegner points 33 6 Heegner points and integration on H p ×H q 40 7 Periods of Hilbert modular forms 48 Introduction Let E be an elliptic curve over Q of conductor N . By the fundamental work initiated in [Wi] and brought to a successful conclusion in [BCDT], the curve E is equipped with a non-constant complex uniformisation Φ: H/Γ 0 (N )−→E(C), (1) 1