Hasse principle for simply connected groups

Abstract: Hasse principle for the isotropy of quadratic forms over number fields is the classical theorem of Hasse-Minkowski. We describe Kneser's conjectures on Hasse principle for simply connected groups over number fields and a conjecture of Serre in the general context of cohomological dimension 2 fields placing Kneser's conjecture in a very general context. We then describe questions and conjectures for function fields of curves over p-adic and number fields and some progress in this direction.

algebraic geometrydifferential geometrygroup theorygeometric topologynumber theory

Audience: general audience

International Conference on Discrete groups, Geometry and Arithmetic

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