An equivariant compactification for adjoint reductive group schemes
Abstract
Wonderful compactifications of adjoint reductive groups over an algebraically closed field play an important role in algebraic geometry and representation theory. In this paper, we construct an equivariant compactification for adjoint reductive groups over arbitrary base schemes. Our compactifications parameterize classical wonderful compactifications of De Concini and Procesi as geometric fibers. Our construction is based on a variant of the Artin-Weil method of birational group laws. In particular, our construction gives a new intrinsic construction of wonderful compactifications. The Picard group scheme of our compactifications is computed. We also discuss several applications of our compactification in the study of torsors under reductive group schemes.
Cite
@article{arxiv.2308.01715,
title = {An equivariant compactification for adjoint reductive group schemes},
author = {Shang Li},
journal= {arXiv preprint arXiv:2308.01715},
year = {2025}
}
Comments
no major change, add section 6.4, the long proof of Theorem 5.1 is decomposed into several small lemmas, the index of f in the proof of Lemma 3.2 is corrected