Good reduction of algebraic groups and flag varieties

TL;DR

This paper explores the finiteness of algebraic groups and flag varieties with good reduction outside a fixed set of places, extending Faltings' finiteness results from abelian varieties to broader classes.

Contribution

It generalizes Faltings' finiteness theorem to algebraic groups and flag varieties, establishing conditions for good reduction in these contexts.

Findings

Finiteness results for algebraic groups with good reduction

Extension of Faltings' theorem to flag varieties

Conditions for good reduction outside specified places

Abstract

In 1983, Faltings proved that there are only finitely many abelian varieties over a number field of fixed dimension and with good reduction outside a given set of places. In this paper, we consider the analogous problem for other algebraic groups and their homogeneous spaces, such as flag varieties.