BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Bett (Harvard University) DTSTART:20230607T010000Z DTEND:20230607T020000Z DTSTAMP:20260423T024655Z UID:PekiNT/8 DESCRIPTION:Title: p -adic obstructions and Selmer sections\nby Alexander Bett (Harvard Uni versity) as part of PKU/BICMR Number Theory Seminar\n\n\nAbstract\nIn 1983 \, shortly after Faltings' resolution of the Mordell Conjecture\, Grothend ieck formulated his famous Section Conjecture\, positing that the set of r ational points on a projective curve Y of genus at least two should be equ al to a certain section set defined in terms of the etale fundamental grou p of Y. To this day\, this conjecture remains wide open\, with only a smal l handful of very special examples known. In this talk\, I will discuss re cent work with Jakob Stix\, in which we proved a Mordell-like finiteness t heorem for the "Selmer" part of the section set for any smooth projective curve Y of genus at least 2 over the rationals. This generalises the Falti ngs-Mordell Theorem\, and implies strong constraints on the finite descent locus from obstruction theory. The key new idea in our proof is an adapta tion of the recent proof of Mordell by Lawrence and Venkatesh to the study of the Selmer section set. Time permitting\, I will also briefly describe recent work with Theresa Kumpitsch and Martin Lüdtke in which we compute the Selmer section set in one example using the Chabauty-Kim method.\n\nO nline only. The Zoom number is 743 736 2326\, and the password is 013049.\ n LOCATION:https://researchseminars.org/talk/PekiNT/8/ END:VEVENT END:VCALENDAR