Explicit descent on elliptic curves and splitting Brauer classes

Benjamin Antieau; Asher Auel

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arXiv · 2106.04291

Explicit descent on elliptic curves and splitting Brauer classes

Benjamin Antieau·Asher Auel

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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.

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Benjamin Antieau, Asher Auel. 2021-06-08. Explicit descent on elliptic curves and splitting Brauer classes. https://arxiv.org/abs/2106.04291

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