Varieties of modules of \(F\)-sheaves. (English. Russian original) Zbl 0665.12013

Drinfel’d, V. G.

Funct. Anal. Appl. 21, No. 1-3, 107-122 (1987); translation from Funkts. Anal. Prilozh. 21, No. 2, 23-41 (1987).

This article is the first in a series of papers aiming to prove a part of the Langlands conjecture for \(\mathrm{GL}(2)\) over a global field \(k\) of characteristic \(p>0.\) More precisely, one wants to construct a map \(\Sigma_ 2\to \Sigma_ 1\) where: \(\Sigma_ 1\) is the set of irreducible 2-dimensional representations over \({\overline{\mathbb Q}}_{\ell}\) \((\ell \neq p)\) of the Weyl group of \(k\), continuous in the \(\ell\)-adic topology and with finitely many branching points, and \(\Sigma_ 2\) is the set of irreducible representations of \(\mathrm{GL}(2)\) over the adeles of \(k\) in the space of \({\overline {\mathbb Q}}_{\ell}\)-valued parabolic forms. One of the main methods in order to do this is to study the geometry of the moduli space of \(F\)-modules of rank 2. The paper under review deals precisely with this study.

Reviewer: L.Bădescu

MSC:

11R39	Langlands-Weil conjectures, nonabelian class field theory
14D20	Algebraic moduli problems, moduli of vector bundles
11F70	Representation-theoretic methods; automorphic representations over local and global fields
22E55	Representations of Lie and linear algebraic groups over global fields and adèle rings

Keywords:

irreducible representations; Langlands conjecture; Weyl group; moduli space of \(F\)-modules

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