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SUMMARY:Jane Shi (MIT)
DTSTART:20251016T203000Z
DTEND:20251016T220000Z
DTSTAMP:20260422T220656Z
UID:STAGE/139
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/139/">
 Katz's proof of the Riemann hypothesis for curves</a>\nby Jane Shi (MIT) a
 s part of STAGE\n\nLecture held in Room 2-105 in the MIT Simons Building.\
 n\nAbstract\nIn this talk\, we'll study a proof of the Riemann Hypothesis 
 for (projective\, smooth and  geometrically connected) curves over finite 
 fields by Katz. We'll study Deligne's version of Rankin's method and the "
 connect by curves" lemma\, and how they reduce a proof of RH on genus $g$ 
 curves to a proof of RH on Fermat curves. Finally\, we'll introduce the "p
 ersistence of purity theorem"\, which will be useful for the next talk.\n\
 n(Reference: section 1-4 of <a href="https://doi.org/10.1093/imrn/rnu007">
 A Note on Riemann Hypothesis for Curves and Hypersurfaces Over Finite Fiel
 ds</a>)\n
LOCATION:https://researchseminars.org/talk/STAGE/139/
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