Coherent Tannaka duality and algebraicity of Hom-stacks

TL;DR

This paper proves a form of Tannaka duality for certain algebraic stacks and demonstrates the broad existence of Hom-stacks, advancing the understanding of their structure and properties.

Contribution

It introduces a Tannaka duality framework for noetherian algebraic stacks with affine stabilizers and establishes the existence of Hom-stacks in general settings.

Findings

Tannaka duality holds for noetherian algebraic stacks with affine stabilizers.

Hom-stacks exist in a wide range of algebraic geometric contexts.

The results generalize previous duality and stack existence theorems.

Abstract

We establish Tannaka duality for noetherian algebraic stacks with affine stabilizer groups. Our main application is the existence of Hom-stacks in great generality.