41 citations · 153 across the 33 of their papers we have counts for
14 papers · 1 filter
Hasse principle for intersections of two quadrics via Kummer surfaces
Adam Morgan, Alexei N. Skorobogatov
We prove new cases of the Hasse principle for Kummer surfaces constructed from 2-coverings of Jacobians of genus 2 curves, assuming finiteness of relevant Tate-Shafarevich groups.…
Generic diagonal conic bundles revisited
Alexei N. Skorobogatov, Efthymios Sofos
We prove a stronger form of our previous result that Schinzel's Hypothesis holds for of -tuples of integer polynomials satisfying the usual necessary conditions, where t…
Reduction of Kummer surfaces modulo 2 in the non-supersingular case
Christopher Lazda, Alexei Skorobogatov
We obtain necessary and sufficient conditions for the good reduction of Kummer surfaces attached to abelian surfaces with non-supersingular reduction when the residue field is perf…
Schinzel Hypothesis on average and rational points
Alexei N. Skorobogatov, Efthymios Sofos
We resolve Schinzel's Hypothesis (H) for of polynomials of arbitrary degree. We deduce that a positive proportion of diagonal conic bundles over with any given…
On uniformity conjectures for abelian varieties and K3 surfaces
Martin Orr, Alexei N. Skorobogatov, Yuri G. Zarhin
We discuss logical links among uniformity conjectures concerning K3 surfaces and abelian varieties of bounded dimension defined over number fields of bounded degree. The conjecture…
Hasse principle for generalised Kummer varieties
Yonatan Harpaz, Alexei N. Skorobogatov
The existence of rational points on Kummer varieties associated to 2-coverings of abelian varieties over number fields can sometimes be proved through the variation of the Selmer g…