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Professor Raman (Emory University), Mathematics Colloquium
November 9, 2017 @ 4:00 pm - 5:00 pm
Title: Isotropy of quadratic forms over function fields in one variable over totally imaginary number fields
Abstract: A theorem of Hasse-Minkowski asserts that a quadratic form over a number field is isotropic (i.e., it represents zero nontrivially,) if it is isotropic over all completions of the number field at its places. Similar local-global principle for function fields of curves over totally imaginary number fields would lead to the following: every quadratic form in at least nine variables over such fields is isotropic. It is a big open question whether quadratic forms in large enough number of variables have a nontrivial zero over such fields. We discuss recent approaches to this question and some progress for function fields of p-adic curves.