A moduli space of character sheaves

TL;DR

This paper constructs and analyzes a moduli space of de Rham character sheaves on commutative algebraic groups, exploring their geometric and functorial properties with foundational results on de Rham spaces.

Contribution

It introduces a group algebraic space representing de Rham character sheaves and studies its functoriality and geometric structure, including foundational results on de Rham spaces.

Findings

Construction of the moduli space $G^lat$ for de Rham character sheaves

Analysis of the functoriality and geometric properties of $G^lat$

Elementary proofs of basic de Rham space results

Abstract

We study de Rham character sheaves on a commutative connected algebraic group $G$, defined as multiplicative line bundles with integrable connection. We construct a group algebraic space $G^\flat$ representing their moduli problem on seminormal test schemes, and we investigate its functoriality and geometry. The main technical ingredient is a study of extension sheaves on the de Rham space $G_\text{dR}$. An appendix provides self-contained, elementary proofs of basic results on de Rham spaces that may be of independent interest.