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ON THE SMOOTHNESS OF CENTRALIZERS IN REDUCTIVE GROUPS.
- Source :
-
Transactions of the American Mathematical Society . Jul2013, Vol. 365 Issue 7, p3753-3774. 22p. - Publication Year :
- 2013
-
Abstract
- Let G be a connected reductive algebraic group over an algebraically closed field k. In a recent paper, Bate, Martin, Röhrle and Tange show that every (smooth) subgroup of G is separable provided that the characteristic of k is very good for G. Here separability of a subgroup means that its scheme-theoretic centralizer in G is smooth. Serre suggested extending this result to arbitrary, possibly non-smooth, subgroup schemes of G. The aim of this paper is to prove this more general result. Moreover, we provide a condition on the characteristic of k that is necessary and sufficient for the smoothness of all centralizers in G. We finally relate this condition to other standard hypotheses on connected reductive groups. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 365
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 87073374