Heegner Points, Stark-Heegner Points, and Diagonal Classes
Massimo Bertolini, Henri Darmon, Victor Rotger, "Heegner Points, Stark-Heegner Points, and Diagonal Classes"
English | ISBN: 2856299598 | 2022 | 228 pages | PDF | 5 MB
English | ISBN: 2856299598 | 2022 | 228 pages | PDF | 5 MB
Abstract.—This volume comprises four interrelated articles whose unifying theme is
the study of Heegner and Stark-Heegner points, and their connections with the padic 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.