Rational Homotopy and Hodge Theory of Moduli Stacks of principal $G$-bundles

TL;DR

This paper investigates the rational cohomology and Hodge-Tate structures of moduli stacks of principal G-bundles over certain complex varieties, utilizing homotopy theory of the associated topological stacks.

Contribution

It provides a detailed determination of the rational cohomology and Hodge-Tate structures for these moduli stacks, advancing understanding of their geometric and topological properties.

Findings

Explicit descriptions of rational cohomology for moduli stacks

Identification of Hodge-Tate structures in the context of principal G-bundles

Application of homotopy theory to complex algebraic stacks

Abstract

For a semisimple complex algebraic group $G$ we determine the rational cohomology and the Hodge-Tate structure of the moduli stack ${\mathscr B}un_{G,X}$ of principal $G$-bundles over a connected smooth complex projective variety $X$ of special type using the homotopy theory of the underlying topological stack.