Rationality criteria for motivic zeta functions

By Michael Larsen, V. Lunts. Compositio Mathematica, 2002

57 citations recorded by the source corpus.

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 the Kodaira dimension of the surface is negative.

Subfields: Algebra and Number Theory, Geometry and Topology, Pharmacology

View Paper: https://www.semanticscholar.org/paper/14b9bb3f36a9abd514723085b807aa2f33fa0e9e

How researchers see this paper

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In Algebra and Number Theory

1. Willem Veys
2. J. Heinloth

In Geometry and Topology

1. O. Garc'ia-Prada
2. A. Schmitt
3. Willem Veys
4. J. Heinloth
5. Tamás Hausel
6. S. Rayan
7. Anna Wienhard
8. Joerg Schuermann

In Pharmacology

1. O. Garc'ia-Prada
2. A. Schmitt
3. Willem Veys
4. J. Heinloth

Citations in the corpus

• On the motives of moduli of chains and Higgs bundles (2011, background): “As observed in [27] this extend this to classes in K0(Vark), by Sym([X ] + [Y ]) := ∑”
• Arc spaces, motivic integration and stringy invariants (2004, background): “Larsen and Lunts [ LL1 ][LL2] determined for which surfaces this is a rational function over K0(V arC).”