Parametric rectilinearization for p-adic semi-algebraic sets and rationality of p-adic integrals

TL;DR

This paper introduces a parametric rectilinearization theorem for p-adic semi-algebraic sets and uses it to provide an alternative proof of the rationality of parametric p-adic integrals, enhancing understanding of their structure.

Contribution

It develops a new rectilinearization theorem for p-adic semi-algebraic sets with parameters and applies it to reprove the rationality of parametric p-adic integrals.

Findings

Established a parametric rectilinearization theorem for p-adic semi-algebraic sets.

Provided an alternative proof of the rationality of parametric p-adic integrals.

Enhanced the theoretical framework for analyzing p-adic integrals.

Abstract

We present a rectilinearization theorem for p-adic semi-algebraic sets depending on parameters. As an application of our main theorem we present an alternative proof of a rationality result for parametric p-adic inte- grals, due to Denef.