English

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 GL2\mathrm{GL}_2 over a number field which is not totally real, improving the one obtained by Marshall. The main tool of the proof is the mod pp representation theory of GL2(Qp)\mathrm{GL}_2(\mathbb{Q}_p) 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}
}

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