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

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

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.

References

SHOWING 1-10 OF 34 REFERENCES

Sous-groupe de Brauer invariant et obstruction de descente itérée

For a quasi-projective smooth geometrically integral variety over a number field $k$, we prove that the iterated descent obstruction is equivalent to the descent obstruction. This generalizes a

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

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

Moduli of abelian varieties and p-divisible groups : Density of Hecke orbits, and a conjecture by Grothendieck

Conference on Arithmetic Geometry, Gottingen 17 July - 11 August 2006. In the week 7 – 11 August 2006 we give a course, and here are notes for that course. Our main topic will be: geometry and

Finite descent obstructions and rational points on curves

Let k be a number field and X a smooth projective k-variety. In this paper, we study the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational

On uniformity conjectures for abelian varieties and K3 surfaces

We discuss logical links among uniformity conjectures concerning K3 surfaces and abelian varieties of bounded dimension defined over number fields of bounded degree. The conjectures concern the

Complex Abelian Varieties

Notation.- 1. Complex Tori.- 2. Line Bundles on Complex Tori.- 3. Cohomology of Line Bundles.- 4. Abelian Varieties.- 5. Endomorphisms of Abelian Varieties.- 6. Theta and Heisenberg Groups.- 7.

Moduli of supersingular abelian varieties

Supersingular abelian varieties.- Some prerequisites about group schemes.- Flag type quotients.- Main results on S g,1.- Prerequisites about Dieudonne modules.- PFTQs of Dieudonne modules over W.-

Hecke orbits on Siegel modular varieties

We sketch a proof of the Hecke orbit conjecture for the Siegel modular variety \(\mathcal{A}_{g,n}\) over \(\overline {\mathbb{F}_p }\), where p is a prime number, fixed throughout this article. We

Linear representations of finite groups

Representations and characters: generalities on linear representations character theory subgroups, products, induced representation compact groups examples. Representations in characteristic zero: