Compactification of Reductive Group Schemes

Ayan Nath

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arXiv · 2601.22462

Compactification of Reductive Group Schemes

Ayan Nath

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Abstract

Let $\mathrm G$ be an isotrivial reductive group over a scheme $S$. We construct a smooth projective $S$-scheme containing $\mathrm G$ as a fiberwise-dense open subscheme equipped with left and right actions of $\mathrm G$ which extend the translation actions of $\mathrm G$ on itself. This verifies a conjecture of \v{C}esnavi\v{c}ius (arXiv:2201.06424). When $\mathrm G$ is adjoint, we recover fiberwise the wonderful compactification. Finally, we give an example of a non-isotrivial torus admitting no equivariant compactification.

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Ayan Nath. 2026-01-30. Compactification of Reductive Group Schemes. https://arxiv.org/abs/2601.22462

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