Geometric class field theory and Cartier duality

TL;DR

This paper develops a generalized Albanese property for curves over any field, connecting it with Cartier duality, and reestablishes local and global geometric class field theory with arbitrary ramification.

Contribution

It introduces a new formulation of the Albanese property for families of maps into commutative group stacks and links it to Cartier duality, providing a unified proof of class field theory.

Findings

Proves a generalized Albanese property for smooth curves over arbitrary fields.

Establishes new Ext-vanishing results used in the proof.

Reproves local and global geometric class field theory with arbitrary ramification.

Abstract

We formulate and prove a generalized Albanese property for families of maps from a smooth curve over an arbitrary field into a commutative group stack. Our proof, which is mostly self-contained, employs local-to-global techniques and some new Ext-vanishing results to reduce to the local Cartier self-duality theorem of Contou-Carrere. As a corollary, we reprove local and global geometric class field theory with arbitrary ramification.