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math.AG2026
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…
math.AG2022
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…