Good reduction of algebraic groups and flag varieties
Ariyan Javanpeykar, Daniel Loughran

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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Coding theory and cryptography
