BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Niccolo Ronchetti (University of California\, Los Angeles) DTSTART:20200604T210000Z DTEND:20200604T220000Z DTSTAMP:20260423T041113Z UID:UCSD_NTS/7 DESCRIPTION:Title: A derived Hecke action on the ordinary Hida tower\nby Niccolo Ronchet ti (University of California\, Los Angeles) as part of UCSD number theory seminar\n\nLecture held in APM 7321.\n\nAbstract\nWhen studying the cohomo logy of Shimura varieties and arithmetic manifolds\, one encounters the fo llowing phenomenon: the same Hecke eigensystem shows up in multiple degree s around the middle dimension\, and its multiplicities in these degrees re sembles that of an exterior algebra.\n\nIn a series of recent papers\, Ven katesh and his collaborators provide an explanation: they construct graded objects having a graded action on the cohomology\, and show that under go od circumstances this action factors through that of an explicit exterior algebra\, which in turn acts faithfully and generate the entire Hecke eige nspace.\n\nIn this talk\, we discuss joint work with Khare where we invest igate the $p=p$ situation (as opposed to the $l \\neq p$ situation\, which is the main object of study of Venkatesh’s Derived Hecke Algebra paper) : we construct a degree-raising action on the cohomology of the ordinary H ida tower and show that (under some technical assumptions)\, this action g enerates the full Hecke eigenspace under its lowest nonzero degree. Then\, we bring Galois representations into the picture\, and show that the deri ved Hecke action constructed before is in fact related to the action of a certain dual Selmer group.\n\nThere will be a pre-talk.\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/7/ END:VEVENT END:VCALENDAR