# Invariant Brauer group of an abelian variety

@article{Orr2022InvariantBG, title={Invariant Brauer group of an abelian variety}, author={Martin Orr and Alexei N. Skorobogatov and Domenico Valloni and Yuri G. Zarhin}, journal={Israel Journal of Mathematics}, year={2022} }

We study a new object that can be attached to an abelian variety or a complex torus: the invariant Brauer group, as recently defined by Yang Cao. Over an algebraically closed field of characteristic different from 2 this is an elementary abelian 2-group with an explicit upper bound on the rank. We exhibit many cases in which the invariant Brauer group is zero, and construct simple complex abelian varieties in every dimension starting with 3, as well as both simple and non-simple complex abelian…

## 3 Citations

### Sous-groupe de Brauer invariant pour un groupe alg\'ebrique connexe quelconque

- Mathematics
- 2018

In this paper, for a smooth variety equiped with an action of a connected algebraic group (not necessary linear), we introduce the notion of invariant Brauer sub-group and the notion of invariant…

### Simple Complex Tori of Algebraic Dimension 0

- Mathematics
- 2021

Using Galois theoory, we construct explicitly (in all complex dimensions ≥ 2) an infinite family of simple complex tori of algebraic dimension 0 with Picard number 0.

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