Lemma 64.31.6 (03VX)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 64: The Trace Formula
Section 64.31: Automorphic forms and sheaves
Lemma 64.31.6 (cite)

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Lemma 64.31.6. Algebraicity of eigenvalues. If $\Lambda$ is a field then the eigenvalues $t_ v$ for $f\in C(\Lambda )$ are algebraic over the prime subfield $\mathbf{F} \subset \Lambda$ .

Proof. Follows from Proposition 64.31.5. $\square$

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