• Corpus ID: 227255062

On geometric Brauer groups and Tate-Shafarevich groups.

@article{Qin2020OnGB,
  title={On geometric Brauer groups and Tate-Shafarevich groups.},
  author={Yanshuai Qin},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}
  • Yanshuai Qin
  • Published 3 December 2020
  • Mathematics
  • arXiv: Algebraic Geometry
Let $X$ be a smooth projective variety over a finitely generated field $K$ of characteristic $p>0$. We proved that the finiteness of the $\ell$-primary part of $\mathrm{Br}(X_{K^s})^{G_K}$ for a single prime $\ell\neq p$ will imply the finiteness of the prime-to-$p$ part of $\mathrm{Br}(X_{K^s})^{G_K}$, generalizing a theorem of Tate and Lichtenbaum for varieties over finite fields. For an abelian variety $A$ over $K$, we proved a similar result for the Tate-Shafarevich group of $A… 
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