at the

American Institute of Mathematics, San Jose, California

organized by

Asher Auel, Brendan Hassett, Anthony V'arilly-Alvarado, and Bianca Viray

Elements of the Brauer group arise in the theory of obstructions to the existence of rational points on varieties and to the existence of universal objects of moduli spaces of stable sheaves. The goal of this workshop is to bring together researchers in number theory, complex algebraic geometry, derived categories, and Hodge theory to study connections between these perspectives on Brauer group elements.

The main topics for the workshop are

- Brauer classes arising in twisted derived equivalence as obstructions to rational points.
- Transcendental Brauer classes arising in Brauer--Manin obstructions as providing twisted derived equivalences.
- Explicitly representing Brauer classes as symbols and via non-fine moduli spaces of stable objects.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Abelian n-division fields of elliptic curves and Brauer groups of product Kummer & abelian surfaces

by Anthony Várilly-Alvarado and Bianca Viray, *Forum Math. Sigma 5 (2017), e26, 42 pp. * MR3731278

On a local-global principle for H3 of function fields of surfaces over a finite field

by Alena Pirutka

ACM bundles on cubic fourfolds containing a plane

by Marti Lahoz, Emanuele Macri and Paolo Stellari

Universal spaces for unramified Galois cohomology

by Fedor Bogomolov and Yuri Tschinkel

Derived equivalences and rational points of twisted K3 surfaces

by Kenneth Ascher, Krishna Dasaratha, Alexander Perry, and Rong Zhou, *Brauer groups and obstruction problems, 13–28, Progr. Math., 320, Birkhäuser/Springer, Cham, 2017 * MR3616005

Twisted derived equivalences for affine schemes

by Benjamin Antieau, *Brauer groups and obstruction problems, 7–12, Progr. Math., 320, Birkhäuser/Springer, Cham, 2017 * MR3616004

The Brauer group is not a derived invariant

by Nicolas Addington

Computing Néron-Severi groups and cycle class groups

by Bjorn Poonen, Damiano Testa and Ronald van Luijk, *Compos. Math. 151 (2015), no. 4, 713-734 * MR3334893

Brauer groups on K3 surfaces and arithmetic applications

by by Kelly McKinnie, Justin Sawon, Sho Tanimoto, and Anthony Várilly-Alvarado, *Brauer groups and obstruction problems, 177–218,Progr. Math., 320, Birkhäuser/Springer, Cham, 2017 * MR3616011

Moriwaki divisors and the augmented base loci of divisors on the moduli space of curves

by Salvatore Cacciola, Angelo Felice Lopez and Filippo Viviani, *Michigan Math. J. 65 (2016), no. 3, 533-546 * MR3542764

Unramified Brauer classes on cyclic covers of the projective plane

by Colin Ingalls, Andrew Obus, Ekin Ozman, and Bianca Viray

Universal unramified cohomology of cubic fourfolds containing a plane

by Asher Auel, Jean-Louis Colliot-Th�l�ne and R. Parimala, *Brauer groups and obstruction problems, 29–55, Progr. Math., 320, Birkhäuser/Springer, Cham, 2017 * MR3616006

Descente galoisienne sur le second groupe de Chow : mise au point

by Jean-Louis Colliot-Th�l�ne, *Doc. Math. 2015, Extra vol.: Alexander S. Merkurjev's sixtieth birthday, 195-220 * MR3404380

Hypersurfaces quartiques de dimension 3 : non rationalit� stable

by Jean-Louis Colliot-Th�l�ne and Alena Pirutka, *Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 2, 371-397 * MR3481353

Unirational threefolds with no universal codimension 2 cycle

by Claire Voisin, *Invent. Math. 201 (2015), no. 1, 207-237 * MR3359052