Corpus ID: 235367889

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. 
2 Citations
Twisted Hilbert schemes and division algebras
Let X /S be any Severi–Brauer scheme of constant relative dimension n over a Noetherian base scheme S. For each polynomial φ(t) ∈ Q[t], we construct a scheme Hilb φ(t)(X /S) that étale locally, on aExpand
Genus 1 Curves in Severi--Brauer Surfaces
In a talk at the Banff International Research Station in 2015 Asher Auel asked questions about genus one curves in Severi-Brauer varieties SB(A). More specifically he asked about the smooth cubicExpand

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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
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