BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christian Klevdal (UCSD) DTSTART:20221006T210000Z DTEND:20221006T220000Z DTSTAMP:20260423T022813Z UID:UCSD_NTS/71 DESCRIPTION:Title: Strong independence of $\\ell$ for Shimura varieties\nby Christian K levdal (UCSD) as part of UCSD number theory seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\n(Joint with Stefan Patrikis.) In this talk\ , we discuss a strong form of independence of $\\ell$ for canonical $\\ell $-adic local systems on Shimura varieties\, and sketch a proof of this for Shimura varieties arising from adjoint groups whose simple factors have r eal rank $\\geq 2$. Notably\, this includes all adjoint Shimura varieties which are not of abelian type. The key tools used are the existence of com panions for $\\ell$-adic local systems and the superrigidity theorem of Ma rgulis for lattices in Lie groups of real rank $\\geq 2$. \n\nThe indepen dence of $\\ell$ is motivated by a conjectural description of Shimura vari eties as moduli spaces of motives. For certain Shimura varieties that aris e as a moduli space of abelian varieties\, the strong independence of $\\e ll$ is proven (at the level of Galois representations) by recent work of K isin and Zhou\, refining the independence of $\\ell$ on the Tate module gi ven by Deligne's work on the Weil conjectures.\n\npre-talk at 1:20pm\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/71/ END:VEVENT END:VCALENDAR