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SUMMARY:A higher weight (and automorphic) generalization of the Hermite-Mi
nkowski theorem
DTSTART;VALUE=DATE-TIME:20181212T090000Z
DTEND;VALUE=DATE-TIME:20181212T100000Z
DTSTAMP;VALUE=DATE-TIME:20200602T045424Z
UID:indico-event-4165@indico.math.cnrs.fr
DESCRIPTION:I will show that for any integer N\, there are only finitely m
any cuspidal algebraic automorphic representations of GL_m over Q whose
Artin conductor is N and whose "weights" are in the interval {0\,...\,23}
(with m varying). Via the conjectural yoga between geometric Galois repres
entations (or motives) and algebraic automorphic forms\, this statement ma
y be viewed as a generalization of the classical Hermite-Minkowski theorem
in algebraic number theory. I will also discuss variants of these results
when the base field Q is replaced by an arbitrary number field. \n\nhttp
s://indico.math.cnrs.fr/event/4165/
LOCATION:IHES Centre de conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/4165/
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