Theorem 64.31.3 (03VU)—The Stacks project

Loading web-font TeX/Main/Bold

Table of contents
Part 3: Topics in Scheme Theory
Chapter 64: The Trace Formula
Section 64.31: Automorphic forms and sheaves
Theorem 64.31.3 (cite)

previous theorem
next remark

numberstags

history
statistics
1 tag refers to this tag

Theorem 64.31.3. Suppose $\mathbf{Q}_ l \subset E$ finite, and

$\rho : \pi _1(X)\to \text{GL}_2(E)$

absolutely irreducible, continuous. Then there exists an eigenform $f$ with values in $\overline{\mathbf{Q}}_ l$ whose eigenvalues $t_ v$ , $u_ v$ satisfy the equalities $t_ v = \text{Tr}(\rho (F_ v))$ and $u_ v = q_ v^{-1}\det (\rho (F_ v))$ .

Proof. See [D1]. $\square$

Comments (0)

There are also:

2 comment(s) on Section 64.31: Automorphic forms and sheaves

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment