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SUMMARY:Danielle Wang (MIT)
DTSTART:20200907T190000Z
DTEND:20200907T203000Z
DTSTAMP:20260422T220050Z
UID:STAGE/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/7/">St
 atements of the Weil conjectures\, proof for curves via the Hodge index th
 eorem</a>\nby Danielle Wang (MIT) as part of STAGE\n\n\nAbstract\nReferenc
 es: <a href="https://math.mit.edu/~poonen/papers/Qpoints.pdf">Poonen\, Rat
 ional points on varieties</a>\, Chapter 7 up to Section 7.5.1\; <a href="h
 ttps://www.jmilne.org/math/xnotes/pRH.pdf">Milne\, The Riemann Hypothesis 
 over Finite Fields: from Weil to the present day</a>\, pages 8-10.\n\nThe 
 Weil conjectures concern the zeta functions of varieties over a finite fie
 ld\, which for a smooth proper variety are rational functions that satisfy
  a functional equation and the Riemann hypothesis. The conjectures led to 
 the development of étale cohomology by Grothendieck and Artin. In this ta
 lk\, we will state the Weil conjectures and prove the Riemann hypothesis f
 or curves using the Hodge index theorem.\n
LOCATION:https://researchseminars.org/talk/STAGE/7/
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