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Algebra Seminar

Monday, February 25, 2019 - 3:15pm

Vlerë Mehmeti

University of Caen


University of Pennsylvania

DRL 4N30

Patching was first introduced as an approach to the Inverse Galois Problem. The technique was then extended to a more algebraic setting and used by D. Harbater, J. Hartmann and D. Krashen to prove a local-global principle applicable to quadratic forms. We adapt the method of patching over Berkovich analytic curves to generalize the results of the aforementioned authors. We will begin by introducing the necessary tools from Berkovich's theory: a geometrically flavored approach to non-archimedean analytic geometry which insists on the analogy with the classical complex case. We will then discuss a few of the properties that make patching possible in this setting. Finally, a local-global principle over the function field of a Berkovich curve and its applications to quadratic forms will be presented.