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DTSTAMP:20211206T050436Z
UID:1615467600@ist.ac.at
DTSTART:20210311T140000
DTEND:20210311T150000
DESCRIPTION:Speaker: Raf Cluckers\nhosted by Tim Browning\nAbstract: I will
present joint work with Glazer and Hendel\, which extends the Lang-Weil e
stimates to estimates working with rings of integers modulo powers of prim
es rather than with finite fields (see arxiv). These bounds were found by
Serre in the smooth case\, and by Avni and Aizenbud in the case of rationa
l singularities (which is close to the smooth case). We render the situati
on uniform in the fibers of an algebraic morphism each of whose fibers has
rational singularities. Surprizingly\, this relative case with uniform bo
unds needs rather different methods\, related to motivic integration\, or
more precisely uniform p-adic integration. Subtle new results about formal
ly positive uniform p-adic functions needed to be developed for this to wo
rk.
LOCATION:https://mathseminars.org/seminar/AGNTISTA\, IST Austria
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Raf Cluckers: A number theoretic characterization of (FRS) morphism
s
URL:https://talks-calendar.app.ist.ac.at/events/2977
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