Motivic measures and stable birational geometry

Abstract

We study the motivic Grothendieck group of algebraic varieties from the point of view of stable birational geometry. In particular, we obtain a counter-example to a conjecture of M. Kapranov on the rationality of motivic zeta-function.

13 pages

References in corpus (1)

• The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups

Cited by in corpus (6)

• On some rational generating series occuring in arithmetic geometry
• Birational geometry and derived categories
• The class of the affine line is a zero divisor in the Grothendieck ring: an improvement
• Unramified cohomology, $\A^1$-connectedness, and Chevalley-Warning problem in Grothendieck ring
• Conics in the Grothendieck ring
• On the Grothendieck ring of varieties in positive characteristic