On the p-adic integration over Igusa towers of Siegel modular varieties

TL;DR

This paper develops a detailed p-adic integration framework for Igusa towers of Siegel modular varieties, enabling new applications in explicit reciprocity laws within number theory.

Contribution

It introduces an explicit p-adic integration theory tailored for Igusa towers of Siegel modular varieties, advancing the understanding of their arithmetic properties.

Findings

Established a new p-adic integration method for Igusa towers

Applied the theory to derive explicit reciprocity laws

Enhanced tools for arithmetic geometry of modular varieties

Abstract

We develop an explicit $p$-adic integration theory for Igusa towers of modular Siegel manifolds, which finds applications to explicit reciprocity laws.