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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

References

1. Angéniol, B., Familles de cycle algébriques-schéma de Chow, Lecture Notes in Mathematics, Volume 896 (Springer, 1981).Google Scholar
2. Buchstaber, V. M. and Rees, E. G., The Gelfand map and symmetric products, Selecta Math. 8(4) (2002), 523–535.Google Scholar
3. Deligne, P., Cohomologie a support propre, SGA 4, Exposé XVII, Lecture Notes in Mathematics, Volume 305 (Springer, 1972).Google Scholar
4. Ducrot, F., Cube structures and intersection bundles, J. Pure Appl. Alg. 195 (2005), 33–73.CrossRefGoogle Scholar
5. Elkik, R., Fibrés d'intersections et intégrales de classes the Chern, Annales Scient. Éc. Norm. Sup. 22 (1989), 195–226.Google Scholar
6. Ferrand, D., Un foncteur norme, Bull. Soc. Math. France 126 (1998), 1–49.CrossRefGoogle Scholar
7. Grothendieck, A., Élements de géométrie algébrique, Publications Mathématiques de l'IHÉS, No. 8 (IHÉS, Bures-sur-Yvette, 1961).Google Scholar
8. Iversen, B., Linear determinants with applications to the Picard scheme of a family of algebraic curves, Lecture Notes in Mathematics, Volume 174 (Springer, 1970).Google Scholar
9. Knutson, D., Algebraic spaces, Lecture Notes in Mathematics, Volume 203 (Springer, 1971).Google Scholar
10. Laksov, D., Notes on divided powers, preprint (available at www.math.kth.se/~laksov/notes/divpotensall.pdf).Google Scholar
11. Muñoz-Garcia, E., Fibrés d'intersections, Compositio Math. 124 (2000), 219–252.CrossRefGoogle Scholar
12. Roby, N., Lois polynomes et lois formelles en théorie des modules, Annales Scient. Éc. Norm. Sup. 80 (1963), 213–348.Google Scholar
13. Rydh, D., Families of zero cycles and divided powers, I, Representability, preprint (arXiv:0803.0618).Google Scholar
14. Rydh, D., Families of zero cycles and divided powers, II, The universal family, preprint (available at www.math.kth.se/~dary).Google Scholar
15. Rydh, D., Hilbert and Chow schemes of points, symmetric products and divided powers, preprint (available at www.math.kth.se/~dary).Google Scholar
16. Rydh, D., Noetherian approximation of algebraic spaces and stacks, preprint (arXiv:math/ 0904.0227).Google Scholar
17. Vaccarino, F., Homogeneous multiplicative polynomial laws are determinants, J. Pure Appl. Alg. 213(7) (2009), 1283–1289.Google Scholar