Groups of components and Weil restriction

TL;DR

This paper investigates how the group of connected components of the special fiber of smooth group schemes behaves under Weil restriction, with applications to Néron models.

Contribution

It provides a general description of the behavior of connected components under Weil restriction for smooth group schemes over local rings.

Findings

Characterizes the behavior of connected components under Weil restriction.

Applies results to the theory of Néron models.

Extends understanding of group schemes over local rings.

Abstract

We determine the behavior under Weil restriction of the group of connected components of the special fiber of an arbitrary smooth group scheme (whose Weil restriction exists) over an arbitrary (commutative and unital) local ring. Applications to N\'eron models are given.