Explicit descent on elliptic curves and splitting Brauer classes

Abstract

We prove new results on splitting Brauer classes by genus 1 curves, settling in particular the case of degree 7 classes over global fields. Though our method is cohomological in nature, and proceeds by considering the more difficult problem of splitting ${\mu }_N$-gerbes, we use crucial input from the arithmetic of modular curves and explicit $N$-descent on elliptic curves.

31 pages, comments very welcome!

Cited by in corpus (1)

• Genus 1 Curves in Severi--Brauer Surfaces