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SUMMARY:Margaret Bilu (NYU)
DTSTART;VALUE=DATE-TIME:20200612T174500Z
DTEND;VALUE=DATE-TIME:20200612T184500Z
DTSTAMP;VALUE=DATE-TIME:20221209T122340Z
UID:agstanford/14
DESCRIPTION:Title: Arithmetic and motivic statistics via zeta functions\nby Margaret
Bilu (NYU) as part of Stanford algebraic geometry seminar\n\n\nAbstract\nT
he Grothendieck group of varieties over a field $k$ is the quotient of the
free abelian group on isomorphism classes of algebraic varieties over k b
y the so-called cut-and-paste relations. Many results in number theory hav
e a natural motivic analogue which can be formulated in the Grothendieck r
ing of varieties. For example\, Poonen's finite field Bertini theorem has
a motivic counterpart due to Vakil and Wood\, though none of the two state
ments can be deduced from the other. We describe a conjectural way to unif
y the number-theoretic and motivic statements (when the base field is fini
te) in this and other examples\, and will provide some evidence towards it
. A key step is to reformulate everything in terms of convergence of zeta
functions of varieties in several different topologies. This is joint work
with Ronno Das and Sean Howe.\n
LOCATION:https://researchseminars.org/talk/agstanford/14/
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