Year: 2026
Type: article
Abstract: We prove that the Weil representation over a non-archimedean local field can be realized with coefficients in a number field. We give an explicit descent argument to describe precisely which number field the Weil representation descends to. Our methods also apply over more general coefficient fields, such as $\ell $ -modular coefficient fields, as well as coefficient rings, such as rings of integers, that is, in families. We also prove that the theta correspondence over a perfect field is valid if and only if it is valid over the algebraic closure of this perfect field. These two results together show that the classical local theta correspondence is rational in the sense that it can be defined over a number field and it is compatible to Galois automorphism.
Source: Canadian Journal of Mathematics
Author: Justin Trias
Institution: Aix-Marseille Université
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7156310871
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