For every fan supported in the negative Weyl chamber, universal equivariant toroidal embeddings of split reductive group schemes over Z exist and specialize to the classical embeddings over every algebraically closed field.
Reductive group schemes
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Toroidal embedding of Chevalley groups over $\mathbb{Z}$
For every fan supported in the negative Weyl chamber, universal equivariant toroidal embeddings of split reductive group schemes over Z exist and specialize to the classical embeddings over every algebraically closed field.