Astérisque, n° 434. Heegner points, Stark-Heegner points, and diagonal classes

This volume comprises four interrelated articles whose unifying theme is the study of Heegner and Stark-Heegner points, and their connections with the p -adic logarithm of certain global cohomology classes attached to a pair of weight one theta series of a common (imaginary or real) quadratic field. These global classes are obtained from p -adic deformations of diagonal classes attached to triples of modular forms of weight > 1, and naturally generalise a construction of Kato which one recovers when the two theta series are replaced by Eisenstein series of weight one. Understanding the extent to which such classes obtained via the p -adic interpolation of motivic cohomology classes are themselves motivic is a key motivation for this study. A second is the desire to show that Stark-Heegner points, whose global nature is still poorly understood theoretically, arise from classes in global Galois cohomology.