Tufts Algebra, Geometry, and Number Theory Seminar
2023-02-27
Speaker: Asher Auel (Dartmouth)
Title: Brauer classes split by genus one curves
Abstract: It is an open problem, even over the rational numbers, to decide whether every Brauer class is split by the function field of a genus one curve. The problem has been solved for Brauer classes of index at most 6 over any field. In this talk, I’ll report on work with Ben Antieau relating the problem to the arithmetic of modular curves and methods from explicit descent for elliptic curves, which in particular allow us to solve the case of index 7 over number fields.