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Finite Flat Group Schemes over Local Artin Rings

Published online by Cambridge University Press:  04 December 2007

René Schoof
René Schoof
Affiliation:
Dipartimento di Matematica, 2a Università di Roma ‘Tor Vergata’, I-00133 Rome, Italy. E-mail: schoof@wins.uva.nl
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Abstract

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Let R be a local Artin ring with maximal ideal $\frak m$ and residue class field of characteristic p > 0. We show that every finite flat group scheme over R is annihilated by its rank, whenever $\frak m$p = p$\frak m$ = 0. This implies that any finite flat group scheme over an Artin ring the square of whose maximal ideal is zero, is annihilated by its rank.

Keywords

group schemeHopf algebradeformations
Type
Research Article
Information
Compositio Mathematica , Volume 128 , Issue 1 , August 2001 , pp. 1 - 15
Copyright
© 2001 Kluwer Academic Publishers