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Article Dans Une Revue Algebraic Geometry Année : 2022

Moduli of connections on smooth varieties

Tony Pantev
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Résumé

This paper is a companion to [Pa-To]. We study the moduli functor of flat bundles on smooth, possibly non-proper, algebraic variety X (over a field of characteristic zero). For this we introduce the notion of formal boundary of X, denoted by ∂X, which is a formal analogue of the boundary at ∞ of the Betti topological space associated to X studied in [Pa-To]. We explain how to construct two derived moduli functors Vect (X) and Vect (∂X), of flat bundles on X and on ∂X, as well as a restriction map R : Vect (X) −→ Vect (∂X). This work contains two main results. First of all we prove that the morphism R comes equipped with a canonical shifted lagrangian structure in the sense of [PTVV]. This first result can be understood as the de Rham analogue of the existence of Poisson structures on moduli of local systems studied in [Pa-To]. As a second statement, we prove that the geometric fibers of R are representable by quasi-algebraic spaces, a slight weakening of the notion of algebraic spaces.
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hal-02003691 , version 1 (01-02-2019)

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Tony Pantev, Bertrand Toën. Moduli of connections on smooth varieties. Algebraic Geometry, 2022, ⟨10.14231/AG-2022-009⟩. ⟨hal-02003691⟩
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