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Hasse principle for Kummer varieties in the case of generic 2-torsion

Date(s)
Wednesday 26th March 2025 (14:00-15:00)
Contact
Event Convenor Contact: christian.wuthrich@nottingham.ac.uk

Description
Speaker's Name: Adam Morgan
Speaker's Affiliation: Cambridge
Speaker's Research Theme(s): Pure Mathematics,
Abstract:
Conditional on finiteness of relevant Shafarevich-Tate groups, Harpaz and Skorobogatov established the Hasse principle for Kummer varieties associated to a 2-covering of a principally polarised abelian variety A, under certain large image assumptions on the Galois action on A[2]. However, their method stops short of treating the case where the image is the full symplectic group, due to the possible failure of the Shafarevich-Tate group to have square order in this setting. I will explain work that overcomes this obstruction by combining second descent ideas of Harpaz with new results on the 2-parity conjecture

Venue: Physics C05

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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