BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daniel Gulotta (Max Planck Institute Bonn) DTSTART:20210127T160000Z DTEND:20210127T170000Z DTSTAMP:20260423T024748Z UID:hnts/19 DESCRIPTION:Title: Va nishing theorems for Shimura varieties at unipotent level and Galois repre sentations\nby Daniel Gulotta (Max Planck Institute Bonn) as part of H eilbronn number theory seminar\n\n\nAbstract\nThe Langlands correspondence relates automorphic forms and Galois representations --- for example\, th e modular form $\\eta(z)^2 \\eta(11z)^2$ and the Tate module of the ellipt ic curve $y^2 + y = x^3 - x^2 - 10x - 20$ are related in the sense that th ey have the same L-function. The p-adic Langlands program aims to interpo late the Langlands correspondence in p-adic families. In this setting\, t he role of automorphic forms is played by the completed cohomology groups defined by Emerton.\n\nCalegari and Emerton have conjectured that the comp leted cohomology vanishes above a certain degree\, often denoted $q_0$. I n the case of Shimura varieties of Hodge type\, Scholze has proved the con jecture for compactly supported completed cohomology. We give a strengthe ning of Scholze's result under the additional assumption that the group be comes split over $\\mathbb{Q}_p$. More specifically\, we show that the co mpactly supported cohomology vanishes not just at full infinite level at p \, but also at unipotent level at p.\n\nWe also give an application of the above result to eliminating the nilpotent ideal in certain cases of Schol ze's construction of Galois representations.\n\nThis talk is based on join t work with Ana Caraiani and Christian Johansson and on joint work with An a Caraiani\, Chi-Yun Hsu\, Christian Johansson\, Lucia Mocz\, Emanuel Rein ecke\, and Sheng-Chi Shih.\n LOCATION:https://researchseminars.org/talk/hnts/19/ END:VEVENT END:VCALENDAR