Rationality criteria for motivic zeta-functions

Details Rationality criteria for motivic zeta-functions Rationality criteria for motivic zeta-functions

2002-12-11

arxiv.org/abs/math/0212158v1

Mathematics

Algebraic Geometry

26 pages

Scientific paper

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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