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SUMMARY:Francesc Fité
DTSTART:20201019T190000Z
DTEND:20201019T203000Z
DTSTAMP:20260422T220248Z
UID:STAGE/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/13/">D
 eligne's version of the Rankin method</a>\nby Francesc Fité as part of ST
 AGE\n\n\nAbstract\nWe will present a proof of the Riemann hypothesis for s
 mooth and projective curves defined over a finite field due to Katz. The p
 roof reduces the general case to the case of Fermat curves via a deformati
 on argument (the "connect by curves lemma") and the use of Deligne's versi
 on of the Rankin method. For the case of Fermat curves\, we will recall ho
 w the Riemann hypothesis amounts to a classical well-known result about th
 e size of Jacobi sums.\n\nReference: <a href="https://doi.org/10.1093/imrn
 /rnu007">Katz\, A note on Riemann hypothesis for curves and hypersurfaces 
 over finite fields</a>\, Sections 1-4.\n
LOCATION:https://researchseminars.org/talk/STAGE/13/
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