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SUMMARY:Raf Cluckers (University of Lille\, FR\, KU Leuven\, BE)
DTSTART:20210311T130000Z
DTEND:20210311T140000Z
DTSTAMP:20260423T005756Z
UID:AGNTISTA/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGNTISTA/27/
 ">A number theoretic characterization of (FRS) morphisms</a>\nby Raf Cluck
 ers (University of Lille\, FR\, KU Leuven\, BE) as part of Algebraic Geome
 try and Number Theory seminar - ISTA\n\n\nAbstract\nI will present joint w
 ork with Glazer and Hendel\, which extends the Lang-Weil estimates to esti
 mates working with rings of integers modulo powers of primes rather than w
 ith finite fields (see arxiv). These bounds were found by Serre in the smo
 oth case\, and by Avni and Aizenbud in the case of rational singularities 
 (which is close to the smooth case). We render the situation uniform in th
 e fibers of an algebraic morphism each of whose fibers has rational singul
 arities. Surprizingly\, this relative case with uniform bounds needs rathe
 r different methods\, related to motivic integration\, or more precisely u
 niform p-adic integration. Subtle new results about formally positive unif
 orm p-adic functions needed to be developed for this to work.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/27/
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