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SUMMARY:Kenta Suzuki (Princeton University)
DTSTART:20251120T213000Z
DTEND:20251120T230000Z
DTSTAMP:20260422T220628Z
UID:STAGE/144
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/144/">
 Weights and the statement of Weil II</a>\nby Kenta Suzuki (Princeton Unive
 rsity) as part of STAGE\n\nLecture held in Room 2-105 in the MIT Simons Bu
 ilding.\n\nAbstract\nThe Weil conjecture states that given a smooth projec
 tive variety over a finite field\, the Frobenius eigenvalues on the étale
  cohomology have specific absolute values. As is usual in algebraic geomet
 ry\, we may ask for a relative analog: what happens when there is a morphi
 sm of schemes? We will introduce weights for étale sheaves on schemes and
  formulate Weil II\, which gives a relation between the weights of a sheaf
  to its pushforward. We will see how this recovers the Weil conjecture\, a
 nd record other consequences such as semisimplicity.\n\nReference:\n\n1. S
 zamuely\, Section 7.1-7.2.\n\n2. Kiehl-Weissauer\, <a href = "https://link
 .springer.com/book/10.1007/978-3-662-04576-3"> Weil Conjectures\, Perverse
  Sheaves and $l$-adic Fourier Transform</a>\, Section I.2\, I.7.\n\n3. Del
 igne\, Weil II.\n
LOCATION:https://researchseminars.org/talk/STAGE/144/
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