Index reduction for Brauer classes via stable sheaves (with an appendix by Bhargav Bhatt)

@article{Krashen2007IndexRF,
  title={Index reduction for Brauer classes via stable sheaves (with an appendix by Bhargav Bhatt)},
  author={Daniel Krashen and Max Lieblich},
  journal={arXiv: Algebraic Geometry},
  year={2007}
}
We use twisted sheaves to study the problem of index reduction for Brauer classes. In general terms, this problem may be phrased as follows: given a field $k$, a $k$-variety $X$, and a class $\alpha \in \Br(k)$, compute the index of the class $\alpha_{k(X)} \in \Br(X)$ obtained from $\alpha$ by extension of scalars to $k(X)$. We give a general method for computing index reduction which refines classical results of Schofield and van den Bergh. When $X$ is a curve of genus 1, we use Atiyah's… Expand
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