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SUMMARY:Jack Miller (Harvard)
DTSTART:20251106T213000Z
DTEND:20251106T230000Z
DTSTAMP:20260422T220728Z
UID:STAGE/142
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/142/">
 Deligne's proof in Weil I (Lefschetz pencil)</a>\nby Jack Miller (Harvard)
  as part of STAGE\n\nLecture held in Room 2-105 in the MIT Simons Building
 .\n\nAbstract\nThe main player in this talk is the notion of a <em>Lefsche
 tz pencil</em>\, a special kind of 1-parameter family of varieties with ni
 ce degeneration properties. Because we have discussed how the Riemann Hypo
 thesis for varieties over finite fields reduces to studying the middle coh
 omology of an even dimensional variety\, we will produce a Lefschetz fibra
 tion with odd dimensional fibers whose middle cohomology contains an "inte
 resting piece\," which we will show has big symplectic monodromy.\n\nRefer
 ence: Milne\, <a href = "https://www.jmilne.org/math/CourseNotes/LEC.pdf">
  Lectures on Étale Cohomology</a>\, Section 31-32.\n
LOCATION:https://researchseminars.org/talk/STAGE/142/
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