BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rachel Newton (King's College London) DTSTART:20211117T151500Z DTEND:20211117T161500Z DTSTAMP:20260423T005807Z UID:LAGeNT/17 DESCRIPTION:Title: Arithmetic of rational points and zero-cycles on Kummer varieties\nby Rachel Newton (King's College London) as part of Leiden Algebra\, Geometry \, and Number Theory Seminar\n\n\nAbstract\nIn 1970\, Manin observed that the Brauer group Br(X) of a variety X over a number field K can obstruct t he Hasse principle on X. In other words\, the lack of a K-point on X despi te the existence of points over every completion of K is sometimes explain ed by non-trivial elements in Br(X). This so-called Brauer-Manin obstructi on may not always suffice to explain the failure of the Hasse principle bu t it is known to be sufficient for some classes of varieties (e.g. torsors under connected algebraic groups) and conjectured to be sufficient for ra tionally connected varieties and K3 surfaces.\nA zero-cycle on X is a form al sum of closed points of X. A rational point of X over K is a zero-cycle of degree 1. It is interesting to study the zero-cycles of degree 1 on X\ , as a generalisation of the rational points. Yongqi Liang has shown that for rationally connected varieties\, sufficiency of the Brauer-Manin obstr uction to the Hasse principle for rational points over all finite extensio ns of K implies sufficiency of the Brauer-Manin obstruction to the Hasse p rinciple for zero-cycles of degree 1 over K. In this talk\, I will discuss joint work with Francesca Balestrieri where we extend Liang's result to K ummer varieties.\n LOCATION:https://researchseminars.org/talk/LAGeNT/17/ END:VEVENT END:VCALENDAR