Rationality criteria for motivic zeta-functions
Algebraic Geometry
2007-05-23 v1
Abstract
The zeta-function of a complex variety is a power series whose nth coefficient is the nth symmetric power of the variety, viewed as an element in the Grothendieck ring of complex varieties. We prove that the zeta-function of a surface is rational if and only if its Kodaira dimension is negative.
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Cite
@article{arxiv.math/0212158,
title = {Rationality criteria for motivic zeta-functions},
author = {Michael J. Larsen and Valery A. Lunts},
journal= {arXiv preprint arXiv:math/0212158},
year = {2007}
}
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26 pages