Multiplicities of cohomological automorphic forms on $\mathrm{GL}_2$ and mod $p$ representations of $\mathrm{GL}_2(\mathbb{Q}_p)$
Number Theory
2020-04-15 v5 Representation Theory
Abstract
We prove a new upper bound for the dimension of the space of cohomological automorphic forms of fixed level and growing parallel weight on over a number field which is not totally real, improving the one obtained by Marshall. The main tool of the proof is the mod representation theory of as started by Barthel-Livne and Breuil, and developed by Paskunas.
Keywords
Cite
@article{arxiv.1801.10074,
title = {Multiplicities of cohomological automorphic forms on $\mathrm{GL}_2$ and mod $p$ representations of $\mathrm{GL}_2(\mathbb{Q}_p)$},
author = {Yongquan Hu},
journal= {arXiv preprint arXiv:1801.10074},
year = {2020}
}
Comments
Final version