On the local-global principle for reductive groups over semi-global fields

Abstract: By semi-global field, we mean the field of rational functions of a curve over the field of fractions of a complete discrete valuation ring. Such a semi-global field may be completed in various ways. Over the last ten years, the validity of a Hasse principle for principal homogeneous spaces of reductive groups over semi-global fields has been investigated. I shall report on this. In particular we shall see that in this context the principle need not hold for semisimple simply connected groups, whereas it holds for reductive groups whose underlying variety is birational to affine space. [This is joint work with D. Harbater, J. Hartmann, D. Krashen, R. Parimala and V. Suresh.]

algebraic geometrydifferential geometrygroup theorygeometric topologynumber theory

Audience: general audience

International Conference on Discrete groups, Geometry and Arithmetic

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