The Hasse principle for quartic del Pezzo and Kummer surfacesMPIM

by Alexei Skorobogatov (Imperial College London/MPIM)

Wednesday Mar 11, 2026, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

Most results on the Hasse principle for surfaces concern conic bundles, that is, families of conics parameterised by the projective line. Beyond this case, one needs to work with families of torsors for abelian varieties. Assuming finiteness of relevant Tate-Shafarevich groups, we use a method originally due to Swinnerton-Dyer to prove the Hasse principle for certain Kummer surfaces. As a somewhat unexpected application, we obtain the Hasse principle for sufficiently general quartic del Pezzo surfaces. This is joint work with Adam Morgan.