Push-forward of smooth measures and strong Thom stratifications

TL;DR

This paper investigates the properties of measures pushed forward along maps between smooth varieties over p-adic fields, providing an algebro-geometric criterion for the finiteness of their stalks based on cotangent bundle subvarieties.

Contribution

It introduces a new algebro-geometric criterion ensuring finite-dimensionality of measure stalks in p-adic geometry, linked to cotangent bundle subvarieties.

Findings

Criterion guarantees finite-dimensional stalks of measures

Characterization via canonical subvariety of cotangent bundle

Applicable to smooth varieties over p-adic fields

Abstract

We study the collection of measures obtained via push-forward along a map between smooth varieties over p-adic fields. We investigate when the stalks of this collection are finite-dimensional. We provide an algebro-geometric criterion ensuring this property. This criterion is formulated in terms of a canonical subvariety of the cotangent bundle of the source of the map.