Corpus ID: 235367889

Explicit descent on elliptic curves and splitting Brauer classes

  title={Explicit descent on elliptic curves and splitting Brauer classes},
  author={Benjamin Antieau and Asher Auel},
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. 
2 Citations
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  • S. Lang
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1955
A. Weil proved that the geometric Frobenius π = F a of an abelian variety over a finite field with q = pa elements has absolute value √ q for every embedding. T. Honda and J. Tate showed that A 7→ πAExpand