Comparing the Brauer group and the Tate Shafarevich group
Algebraic Geometry
2018-06-05 v3 Number Theory
Abstract
We give a formula relating the order of the Brauer group of a surface fibered over a curve over a finite field to the order of the Tate-Shafarevich group of the Jacobian of the generic fiber. The formula implies that the Brauer group of a smooth and proper surface over a finite field is a square if it is finite.
Cite
@article{arxiv.1712.06249,
title = {Comparing the Brauer group and the Tate Shafarevich group},
author = {Thomas Geisser},
journal= {arXiv preprint arXiv:1712.06249},
year = {2018}
}
Comments
Rewrote the proof to make it more readable. To appear in Journal of the Institute of Mathematics of Jussieu