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Christophe Delaunay

Heuristics on Class groups and on Tate-Shafarevich groups

Abstract: The class group of a number field as well as the Tate-Shafarevich group of an elliptic curve measure, in a way, the "obstruction to the computations being easy": whenever those groups are trivial then, in general, the underlying arithmetic problem can be solved more easily. We will be concerned with the general behaviour of these groups and more specially with questions about their distributions. In fact, one can obtain some conjectural answers based on basic heuristic asumptions.