4 papers
Brauer--Manin obstruction from failure of Kodaira vanishing in positive characteristic
Fabio Bernasconi, Domenico Valloni
We study the Brauer-Manin set of smooth projective surfaces over global fields of positive characteristic for which Kodaira vanishing fails. Our results apply in particular to Rayn…
Differential forms and Brauer classes in positive characteristic
Domenico Valloni
We study -torsion Brauer classes in positive characteristic arising from differential forms. We relate this construction to the Brauer group of supersingular K3 surfaces and ana…
Enriques involutions and Brauer classes
Alexei N. Skorobogatov, Domenico Valloni
We prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In 'generic' cases this gives a bijection between th…
Invariant Brauer group of an abelian variety
Martin Orr, Alexei N. Skorobogatov, Domenico Valloni +1
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 the field of complex numbers…