Vol. 10, No. 1, 2016

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Extension theorems for reductive group schemes

Adrian Vasiu

Vol. 10 (2016), No. 1, 89–115
Abstract

We prove several basic extension theorems for reductive group schemes via extending Lie algebras and via taking schematic closures. We also prove that, for each scheme Y , the category in groupoids of adjoint group schemes over Y whose Lie algebra OY -modules have perfect Killing forms is isomorphic, via the differential functor, to the category in groupoids of Lie algebra OY -modules which have perfect Killing forms and which, as OY -modules, are coherent and locally free.

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Keywords
reductive group schemes, purity, regular rings, Lie algebras
Mathematical Subject Classification 2010
Primary: 14L15
Secondary: 11G18, 14F30, 14G35, 14K10, 14L17, 17B45
Milestones
Received: 6 January 2015
Revised: 11 December 2015
Accepted: 15 December 2015
Published: 14 February 2016
Authors
Adrian Vasiu
Department of Mathematical Sciences
Binghamton University
P.O. Box 6000
Binghamton, NY 13902-6000
United States