Algebraic Geometry Seminar

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Local-Global Principles Over Arithmetic Function Fields

Speaker: David Harbater, University of Pennsylvania

Location: Warren Weaver Hall 201

Date: Tuesday, April 18, 2017, 3:30 p.m.

Synopsis:

Many local-global principles in algebra can be phrased as asserting the existence of a rational point on a variety V over a field F provided that there are points defined over certain overfields of F that are obtained by taking completions. When the variety V is a torsor, the local-global principle can be stated in terms of first Galois cohomology, via a version of the Tate-Shafarevich group. Classically, F is a global field; but generalizations have been considered for more general fields and for higher cohomology. After reviewing known results, the talk will present recent developments in the situation where F is the function field of a variety over a complete discretely valued field.