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International Mathematics Research Notices Advance Access published online on August 19, 2009
International Mathematics Research Notices, doi:10.1093/imrn/rnp126
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Hodge Cohomology of Étale Nori Finite Vector Bundles

Ðoàn Trung Cuong

FB Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany and Institute of Mathematics, 10307 Hanoi, Vietnamy

Correspondence: Correspondence to be sent to: cuong.doan{at}uni-due.de, dtcuong{at}math.ac.vn

Étale Nori finite vector bundles are the bundles defined by representations of a finite étale group scheme in the usual way. In this article, we show that in many cases the dimensions of the Hodge cohomology groups of such a vector bundle and a twist of it by an automorphism of the ground field are the same. This generalizes to the higher rank case the result of Pink–Roessler [13, Proposition 3.5].

Communicated by Prof. Dmitry Kaledin


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