# Explicit descent on elliptic curves and splitting Brauer classes

@inproceedings{Antieau2021ExplicitDO, title={Explicit descent on elliptic curves and splitting Brauer classes}, author={Benjamin Antieau and Asher Auel}, year={2021} }

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

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