Groups of components of N\'eron models of Jacobians and Brauer groups

TL;DR

This paper explores the relationship between the component group of the Néron model of a Jacobian of a curve over a non-archimedean local field and the Brauer group of the curve, revealing new structural insights.

Contribution

It establishes a connection between the component groups of Néron models and the Brauer groups for curves over non-archimedean fields, providing new theoretical understanding.

Findings

Identifies a relationship between Néron component groups and Brauer groups.

Provides structural insights into Jacobians over local fields.

Enhances understanding of arithmetic geometry of curves.

Abstract

Let $X$ be a proper, smooth, and geometrically connected curve over a non-archimedean local field $K$. In this paper, we relate the component group of the N\'eron model of the Jacobian of $X$ to the Brauer group of $X$.