41 citations · 153 across the 33 of their papers we have counts for
3 papers · 1 filter
Singular curves and the etale Brauer-Manin obstruction for surfaces
Yonatan Harpaz, Alexei Skorobogatov
We construct a smooth and projective surface over an arbitrary number field that is a counterexample to the Hasse principle but has the infinite etale Brauer-Manin set. We also con…
Norms as products of linear polynomials
Damaris Schindler, Alexei Skorobogatov
Let F be a number field, and let F\subset K be a field extension of degree n. Suppose that we are given 2r sufficiently general linear polynomials in r variables over F. Let X be t…
Rational points on pencils of conics and quadrics with many degenerate fibres
Tim Browning, Lilian Matthiesen, Alexei Skorobogatov
For any pencil of conics or higher-dimensional quadrics over the rationals, with all degenerate fibres defined over the rationals, we show that the Brauer-Manin obstruction control…