Moduli stacks of quiver connections and non-Abelian Hodge theory

Mahmud Azam; Steven Rayan

Paper

Moduli stacks of quiver connections and non-Abelian Hodge theory

Abstract

In arXiv:2407.11958, a moduli stack parametrizing

--indexed diagrams of Higgs bundles over a base stack

was constructed for any finite simplicial set

, inspiring speculations about extending the non-Abelian Hodge correspondence to these moduli stacks. In the present work, we formalize the de Rham side of this conjectural extension. We construct moduli stacks parametrizing diagrams of bundles with

--connections over a base prestack

, where

can be a fixed number or a parameter. Taking

to be

gives a moduli stack parametrizing diagrams of bundles with connection, while taking it to be a parameter gives a version of Simpson's non-Abelian Hodge filtration for digrams of bundles with connection. We show that when

is a smooth and projective scheme over an algebraically closed field

of characteristic

, these moduli stacks are algebraic and locally of finite presentation, and have affine diagonal.