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SUMMARY:Elia Gorokhovsky (Harvard)
DTSTART:20251211T213000Z
DTEND:20251211T230000Z
DTSTAMP:20260422T220354Z
UID:STAGE/146
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/146/">
 Applications of Weil II</a>\nby Elia Gorokhovsky (Harvard) as part of STAG
 E\n\nLecture held in Room 2-105 in the MIT Simons Building.\n\nAbstract\nW
 e state two applications of Deligne's theory of weights. The first is the 
 semisimplicity theorem\, which states that a lisse\, pure $\\overline{\\Q_
 \\ell}$-sheaf on a normal base over $\\mathbb F_q$ decomposes as a direct 
 sum of irreducible subsheaves over $\\overline{\\mathbb{F}_q}$. The second
  is a very general theorem about equidistribution of Frobenius elements in
  the monodromy group\, which enables proofs of several important results i
 n arithmetic statistics\, such as the Sato-Tate conjecture over function f
 ields and a version of the Cohen-Lenstra heuristics.\n\nReference:\n\n1. S
 zamuely. A Course on the Weil Conjectures\, Section 7.2.\n\n2. Katz. Gauss
  Sums\, Kloosterman Sums\, and Monodromy Groups\, Chapter 3.\n\n3. Deligne
 . Weil II\, Sections 3.4\, 3.5\n\nSee also:\n\n4. Katz\, Sarnak. Random Ma
 trices\, Frobenius Eigenvalues\, and Monodromy.\n
LOCATION:https://researchseminars.org/talk/STAGE/146/
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