Zeta functions, Grothendieck groups, and the Witt ring

Abstract

We prove some results connecting the zeta functions of varieties over finite fields with the big Witt ring over $\mathbb{Z}$. We explore relations with motivic measures and a classical formula of Macdonald on invariants of symmetric products of a variety.

23 pages, submitted for publication. Added reference to Niko Naumann's work. Comments welcome

References in corpus (1)

• Lambda-rings and the field with one element

Cited by in corpus (10)

• Entropy algebras and Birkhoff factorization
• Gamma Spaces and Information
• Local zeta factors and geometries under Spec Z
• Exponentiation of motivic measures
• Derived $\ell$-adic zeta functions
• Homotopy Spectra and Diophantine Equations
• Higher Euler characteristics
• q-deformations of statistical mechanical systems and motives over finite fields
• Multiplicative zeta function and logarithmic point counting over finite fields
• A MacDonald formula for zeta functions of varieties over finite fields