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SUMMARY:Xinyu Zhou (Boston University)
DTSTART:20251113T213000Z
DTEND:20251113T230000Z
DTSTAMP:20260422T220230Z
UID:STAGE/143
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/143/">
 Deligne's proof in Weil I (Completing the proof)</a>\nby Xinyu Zhou (Bosto
 n University) as part of STAGE\n\nLecture held in Room 2-105 in the MIT Si
 mons Building.\n\nAbstract\nIn this talk\, I will finish Deligne's proof o
 f the Riemann Hypothesis by applying all the tools developed in the previo
 us talks. Crucially\, the theory of Lefschetz pencils reduces the problem 
 to a study of certain higher direct images on P^1. We then use the Lefsche
 tz-Picard formula and the Main Lemma to prove an estimate of the Frobenius
 -eigenvalues on the cohomology of the higher direct images\, which is suff
 icient to deduce the Riemann Hypothesis.\n\nReference: Milne\, <a href = "
 https://www.jmilne.org/math/CourseNotes/LEC.pdf"> Lectures on Étale Cohom
 ology</a>\, Section 28 and 33.\n
LOCATION:https://researchseminars.org/talk/STAGE/143/
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