41 citations · 153 across the 33 of their papers we have counts for
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Descent on toric fibrations
Alexei N. Skorobogatov
We describe descent on families of torsors of a constant torus. A recent result of Browning and Matthiesen then implies that the Brauer--Manin obstruction controls the Hasse princi…
Odd order Brauer--Manin obstruction on diagonal quartic surfaces
Evis Ieronymou, Alexei N. Skorobogatov
We determine the odd order torsion subgroup of the Brauer group of diagonal quartic surfaces over the field of rational numbers. We show that a non-constant Brauer element of odd o…
Pathologies of the Brauer-Manin obstruction
Jean-Louis Colliot-Thélène, Ambrus Pál, Alexei N. Skorobogatov
We construct a conic bundle over an elliptic curve over a real quadratic field that is a counterexample to the Hasse principle not explained by the étale Brauer-Manin obstruction.…
The Hardy--Littlewood conjecture and rational points
Yonatan Harpaz, Alexei N. Skorobogatov, Olivier Wittenberg
Schinzel's Hypothesis (H) was used by Colliot-Thélène and Sansuc, and later by Serre, Swinnerton-Dyer and others, to prove that the Brauer-Manin obstruction controls the Hasse prin…