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Norm functors and effective zero cycles

Part of: Families, fibrations Cycles and subschemes

Published online by Cambridge University Press:  12 August 2010

Vladimir Baranovsky
Vladimir Baranovsky
Affiliation:
Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA (vbaranov@math.uci.edu)
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Abstract

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We compare two known definitions for a relative family of effective zero cycles: one based on traces of functions and one based on norms of functions. In characteristic zero we show that both definitions agree. In the general setting we show that the norm map on functions can be expanded to a norm functor between certain categories of line bundles, thereby giving a third approach to families of zero cycles.

Keywords

zero cyclesdeterminant bundlesChow varieties

MSC classification

Secondary: 14C05: Parametrization (Chow and Hilbert schemes) 14D23: Stacks and moduli problems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 3 , October 2010 , pp. 557 - 574
Copyright
Copyright © Edinburgh Mathematical Society 2010

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