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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn045, 17 pages, doi:10.1093/imrn/rnn045 published on May 8, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Bounds for Behrend's Conjecture on the Canonical Reduction

Jochen Heinloth

University of Amsterdam, Korteweg-de Vries Institute for Mathematics, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands

Correspondence: Correspondence to be sent to: heinloth{at}science.uva.nl

We prove Behrend's conjecture on the rationality of the canonical reduction of principal bundles, and reductive group schemes for classical groups and give new bounds for the conjecture for exceptional groups. However, we find a counterexample in the case of G2-bundles in characteristic 2.


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