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On Primitive and Realisable Classes

Published online by Cambridge University Press:  04 December 2007

A. Agboola
A. Agboola
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A. E-mail: agboola@math.ucsb.edu
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Abstract

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Let S be a scheme, and let G be a finite, flat, commutative group scheme over S. In this paper we show that (subject to a mild technical assumption) every primitive class in Pic(G) is realisable. This gives an affirmative answer to a question of Waterhouse. We also discuss applications to locally free classgroups and to Selmer groups of Abelian varieties.

Keywords

class invariantsclassgroupsrealizable classesprimitive classesgroup schemestwisted forms
Type
Research Article
Information
Compositio Mathematica , Volume 126 , Issue 1 , March 2001 , pp. 113 - 122
Copyright
© 2001 Kluwer Academic Publishers