Zoom link
https://huji.zoom.us/j/84721203396?pwd=dWkyVTk0WDhlWlBOdVgxR04rKzM1UT09

Meeting ID: 847 2120 3396
Passcode: 189975

Link to recordings:

https://huji.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?folderID=39fd71c4-753c-4a1a-a955-aeb500acd432

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Talk Title: On the Hasse principle for Kummer varieties  

Abstract: Conditional on finiteness of relevant Shafarevich--Tate groups, Harpaz and Skorobogatov established the Hasse principle for Kummer varieties associated to 2- coverings 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 case. I will explain work in progress which overcomes this obstruction by combining second descent ideas in the spirit of Harpaz and Smith with new results on the 2- parity conjecture.