Mathematical Research Letters

Volume 22 (2015)

Number 1

A note on the arithmetic of residual automorphic representations of reductive groups

Pages: 93 – 109

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n1.a6

Author

Harald Grobner (Fakultät für Mathematik, Universität Wien, Austria)

Abstract

We prove an arithmeticity result for a class of cohomological residual automorphic representations of a general reductive group $G$. More precisely, we show that this class of residual representations is stable under the action of $\mathrm{Aut}(\mathbb{C})$. This complements numerous results on the stability of cohomological cuspidal automorphic representations due by several people. We conclude by showing that the rationality field of such a cohomological residual automorphic representation is a number field.

2010 Mathematics Subject Classification

Primary 11F70, 11F75, 22E47. Secondary 11F67.

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Published 13 April 2015