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Number Theory Seminar
Seminar information archive ～01/17｜Next seminar｜Future seminars 01/18～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2018/12/12
18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Gaëtan Chenevier (CNRS, Université Paris-Sud)
A higher weight (and automorphic) generalization of the Hermite-Minkowski theorem (ENGLISH)
Gaëtan Chenevier (CNRS, Université Paris-Sud)
A higher weight (and automorphic) generalization of the Hermite-Minkowski theorem (ENGLISH)
[ Abstract ]
I will show that for any integer N, there are only finitely many 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 representations (or motives) and algebraic automorphic forms, this statement may 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.
I will show that for any integer N, there are only finitely many 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 representations (or motives) and algebraic automorphic forms, this statement may 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.
