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SUMMARY:Hélène Esnault (FU Berlin/Harvard/Copenhagen)
DTSTART:20231205T210000Z
DTEND:20231205T220000Z
DTSTAMP:20260423T130058Z
UID:MITNT/83
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/83/">S
 urvey on some arithmetic properties of rigid local systems</a>\nby Hélèn
 e Esnault (FU Berlin/Harvard/Copenhagen) as part of MIT number theory semi
 nar\n\nLecture held in Room 2-449 in the Simons Building (building 2).\n\n
 Abstract\nA central conjecture of Simpson predicts that complex rigid loca
 l systems on a smooth complex variety come from geometry. In the last coup
 le of years\, we proved some arithmetic consequences of it: integrality (u
 sing the arithmetic Langlands program)\, F-isocrystal properties\, crystal
 linity of the underlying p-adic representation (using the Cartier operator
  over the Witt vectors and the Higgs-de Rham flow) (for Shimura varieties 
 of real rank at least 2\, this is the corner piece of Pila-Shankar-Tsimerm
 an's proof of the André-Oort conjecture)\, weak integrality of the charac
 ter variety (using de Jong's conjecture proved with the geometric Langland
 s program)  (yielding a new obstruction for a finitely presented group to 
 be the topological fundamental group of a smooth complex variety).\n\nWe'l
 l survey some aspects of this (please ask if there is something on which y
 ou would like me to focus on). The talk is based mostly on joint work with
  Michael Groechenig\, also\, even if less\, with Johan de Jong.\n
LOCATION:https://researchseminars.org/talk/MITNT/83/
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