41 citations · 153 across the 33 of their papers we have counts for
25 papers · 1 filter
Zero-cycles on surfaces dominated by products of hyperelliptic curves
Jean-Louis Colliot-Thélène, Federico Scavia, Alexei Skorobogatov
Conditionally on the finiteness of the relevant Tate-Shafarevich groups, we prove a local-to-global result for zero-cycles of degree on the surfaces given by $y^2 = f_1(x_1)f_2…
Dichotomy for the Brauer-Manin obstruction in characteristic p
Christopher D. Lazda, Alexei N. Skorobogatov
Let X be a smooth, projective, geometrically integral variety over a global function field k of characteristic p. We show that if the unipotent Brauer group of X is zero, and the P…
Brauer groups of abelian varieties over fields of finite characteristic
Livia Grammatica, Alexei N. Skorobogatov, Yuan Yang
We study the Brauer group of an abelian variety A over an algebraically closed field of characteristic p focusing on the p-primary torsion, the key part of which is a certain quasi…
Birational properties of word varieties
Tatiana Bandman, Boris Kunyavskii, Alexei N. Skorobogatov
We prove that the subvariety of given by the matrix equation , where is a word in two letters, is closely related to an explicit smooth conic bund…
On spectral sequences for semiabelian varieties over non-closed fields
Alexander Petrov, Alexei Skorobogatov
We give a new, short proof of the formula for the first potentially non-zero differential of the Hochschild--Serre spectral sequence for semiabelian varieties over non-closed field…
Boundedness of the p-primary torsion of the Brauer groups of K3 surfaces
Christopher D. Lazda, Alexei N. Skorobogatov
We prove that the transcendental Brauer group of a K3 surface X over a finitely generated field k is finite, unless k has positive characteristic p and X is supersingular, in which…