BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Loeffler (Warwick) DTSTART:20201030T143000Z DTEND:20201030T160000Z DTSTAMP:20260423T004700Z UID:CAFAS/8 DESCRIPTION:Title: P- adic interpolation of Gross--Prasad periods and diagonal cycles\nby Da vid Loeffler (Warwick) as part of Columbia Automorphic Forms and Arithmeti c Seminar\n\n\nAbstract\nThe Gross--Prasad conjecture for orthogonal group s relates special values of L-functions for SO(n) x SO(n+1) to period inte grals of automorphic forms. This conjecture is known for n = 3\, in which case the group SO(3) x SO(4) is essentially GL2 x GL2 x GL2\; and the stud y of these GL2 triple product periods\, and in particular their variation in p-adic families\, has had important arithmetic applications\, such as t he work of Darmon and Rotger on the equivariant BSD conjecture for ellipti c curves.\n\nI'll report on work in progress with Sarah Zerbes studying th ese periods in the n = 4 case\, where the group concerned is isogenous to GSp4 x GL2 x GL2. I'll explain a construction of p-adic L-functions interp olating the Gross--Prasad periods in Hida families\, and an 'explicit reci procity law' relating these p-adic L-functions to diagonal cycle classes i n etale cohomology. These constructions are closely analogous to the Euler system for GSp(4) described in Sarah's talk\, but with cusp forms in plac e of the GL2 Eisenstein series.\n LOCATION:https://researchseminars.org/talk/CAFAS/8/ END:VEVENT END:VCALENDAR