On fields of rationality for automorphic representations
Author(s)Shin, Sug Woo; Templier, Nicolas
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Cambridge University Press
Shin, Sug Woo, and Nicolas Templier. “On Fields of Rationality for Automorphic Representations.” Compositio Math. 150, no. 12 (September 11, 2014): 2003–2053.
Author's final manuscript