Submission date: 24 April 2012.

Abstract:

We construct Hrushovski-Kazhdan style motivic integration in certain expansions of ACVF. Such an expansion is typically obtained by adding a full section or a cross-section from the RV-sort into the VF-sort and some (arbitrary) extra structure in the RV-sort. The construction of integration, that is, the inverse of the lifting map L, is rather straightforward. What is a bit surprising is that the kernel of L is still generated by one element, exactly as in the case of integration in ACVF. The overall construction is more or less parallel to the original Hrushovski-Kazhdan construction. As an application, we show uniform rationality of Igusa zeta functions for non-archimedean local fields with unbounded ramification degrees.

Mathematics Subject Classification: 03C60, 11S80

Keywords and phrases:

Full text arXiv 1204.5979: pdf, ps.