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 this problem to the arithmetic of modular curves and methods from explicit descent for elliptic curves.

number theory

Audience: researchers in the topic

CRM-CICMA Québec Vermont Seminar Series

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