Extension theorems for reductive group schemes

Vasiu, Adrian

doi:10.2140/ant.2016.10.89

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Extension theorems for reductive group schemes

Adrian Vasiu

Vol. 10 (2016), No. 1, 89–115

DOI: 10.2140/ant.2016.10.89

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 $O_{Y}$ -modules have perfect Killing forms is isomorphic, via the differential functor, to the category in groupoids of Lie algebra $O_{Y}$ -modules which have perfect Killing forms and which, as $O_{Y}$ -modules, are coherent and locally free.

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

Vol. 10, No. 1, 2016