BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Amnon Besser (Ben-Gurion University/Boston University) DTSTART:20230502T203000Z DTEND:20230502T213000Z DTSTAMP:20260423T125220Z UID:MITNT/73 DESCRIPTION:Title: L ocal contributions to Quadratic Chabauty functions and derivatives of Volo godsky functions with respect to $log(p)$\nby Amnon Besser (Ben-Gurion University/Boston University) as part of MIT number theory seminar\n\nLec ture held in Room 2-449 in the Simons Building (building 2).\n\nAbstract\n Quadratic Chabauty is a method for finding rational points on curves using $p$-adic methods. The quadratic Chabauty function is a function on these rational points\, usually derived from some $p$-adic height\, which is a s um of local terms at finite primes. The main term is the term at $p$ which is a Coleman function\, but in order to make the method work one needs to be able to compute the finite list of possible values of the other contri butions at primes of bad reduction.\n\nVologodsky functions are the genera lisation of Coleman functions to varieties with bad reduction. In this tal k\, which is based on ongoing work with Steffen Muller and Padma Srinivasa n\, I would like to promote the general (and vague) idea that the derivati ve of a Vologodsky integral with respect to the branch of log parameter $l og(p)$ is arithmetically interesting.\n\nAs an example I will show how the local contribution above a prime $q$ to a $p$ adic height can be computed by deriving the $q$-adic contribution to a $q$-adic height and use this t o obtain a computable formula for this contribution using the work of Katz and Litt. In particular\, I will recover a formula of Betts and Dogra for the local contribution to the Quadratic Chabauty function at a prime wher e the completion is a Mumford curve.\n LOCATION:https://researchseminars.org/talk/MITNT/73/ END:VEVENT END:VCALENDAR