Solvable subgroups generated by irreducible families in Aut of quasi-affine varieties are algebraic, implying connected solvable subgroups have derived length at most n+1 and that maximal Borels on A^n are Jonquières groups.
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Generalizes Steinberg's centralizer component description to unipotent elements under non-etale covers, with applications to L-parameter moduli multiplicities, deformation rings, and non-existence of Springer isomorphism for PGL_p in char p.
Ramanujam's theorem is extended from irreducible varieties to arbitrary varieties by refining the notion of dimension for automorphism groups.
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Solvable Automorphism Groups of Varieties
Solvable subgroups generated by irreducible families in Aut of quasi-affine varieties are algebraic, implying connected solvable subgroups have derived length at most n+1 and that maximal Borels on A^n are Jonquières groups.
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Central isogenies and conjugacy classes in reductive groups
Generalizes Steinberg's centralizer component description to unipotent elements under non-etale covers, with applications to L-parameter moduli multiplicities, deformation rings, and non-existence of Springer isomorphism for PGL_p in char p.
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On Ramanujam's Theorem About Finite Dimensional Groups of Automorphisms
Ramanujam's theorem is extended from irreducible varieties to arbitrary varieties by refining the notion of dimension for automorphism groups.