Toroidal embedding of Chevalley groups over ℤ

2025/06/03 by Li, Shang
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.02638

Abstract

The classification of equivariant toroidal embeddings of a reductive group over an algebraically closed field is combinatorial and does not depend on the characteristic of the base field. This suggests that there should exist ``universal'' toroidal embeddings for a Chevalley group scheme over ℤ which specialize to classical toroidal embeddings via base change. In this paper, we establish the existence of ``universal'' equivariant toroidal embeddings for split reductive group schemes over ℤ. We also discuss several geometric properties of these embeddings.

Citations

• Wonderful embedding for group schemes in the Bruhat--Tits theory
• Dual canonical bases and embeddings of symmetric spaces
• An equivariant compactification for adjoint reductive group schemes
• Study of a Z-form of the coordinate ring of a reductive group

Related

• Equivariant K-theory of cellular toroidal embeddings
• Equivariant Derived Categories for Toroidal Group Imbeddings
• Toroidal Embeddings of Right Groups
• Toroidal embeddings and polyhedral divisors
• Toroidalization of Locally Toroidal Morphisms