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Varieties of modules of $$F$$-sheaves. (English. Russian original) Zbl 0665.12013
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
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References:
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