Speaker:
Gaetan Chenevier
Affiliation:
Université Paris-Sud
Date:
Mon, 12/03/2018 - 15:00 - 16:00
Let $E$ be a number field, $N$ an ideal of its ring of integers, and $w \geq 0$ an integer. Consider the set of cuspidal algebraic automorphic representations of $GL_n$ over $E$ whose conductor is $N$, and whose ''weights'' are in the interval $\{0,\dots,w\}$ (with $n$ varying). If the root-discriminant of $E$ is less than a certain explicit function $f$ of $w$, then I show that this set is finite. For instance, we have $f(w)>1$ if, and only if, $w<24$.