There is no degree map for 0-cycles on Artin stacks

Creators: Edidin, Dan; Geraschenko, Anton; Satriano, Matthew

Abstract

We show that there is no way to define degrees of 0-cycles on Artin stacks with proper good moduli spaces so that (1) the degree of an ordinary point is non-zero, and (1) degrees are compatible with closed immersions.

Additional Information

© 2013 Birkhäuser Boston. Received December 4, 2012. Accepted January 25, 2013. Published online May 8, 2013. We would like to thank Tom Graber, who got the second and third authors interested in this problem, and skillfully disposed of many proposed definitions of degree. We are also grateful to BIRS and to the organizers of the Algebraic Stacks: Progress and Prospects workshop, where much of the work on this paper was done. Finally, the authors are grateful to the referee for a number of insightful comments. Supported by an NSF postdoctoral fellowship (DMS-1103788).

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There is no degree map for 0-cycles on Artin stacks

Abstract

Additional Information

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