On fields of rationality for automorphic representations
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Shin_On fields.pdf
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Author(s)
Shin, Sug Woo
Templier, Nicolas
Date Issued
September 2014
Journal
Compositio Mathematica
Publisher
Cambridge University Press
Citation
Shin, Sug Woo, and Nicolas Templier. “On Fields of Rationality for Automorphic Representations.” Compositio Math. 150, no. 12 (September 11, 2014): 2003–2053.
Version
Author's final manuscript
Abstract
This paper proves two results on the field of rationality Q(π) for an automorphic representation π, which is the subfield of C fixed under the subgroup of Aut(C) stabilizing the isomorphism class of the finite part of π. For general linear groups and classical groups, our first main result is the finiteness of the set of discrete automorphic representations π such that π is unramified away from a fixed finite set of places, π[subscript ∞] has a fixed infinitesimal character, and [Q(π):Q] is bounded. The second main result is that for classical groups, [Q(π):Q] grows to infinity in a family of automorphic representations in level aspect whose infinite components are discrete series in a fixed L-packet under mild conditions.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1112/S0010437X14007428
