Generalized semi-invariant distributions on p-adic spaces

TL;DR

This paper explores methods to compute and extend generalized semi-invariant distributions on p-adic spaces, employing homological and algebraic geometric techniques to establish criteria for their extension.

Contribution

It introduces new criteria for extending semi-invariant distributions on p-adic spaces using homological and algebraic geometric methods.

Findings

Homological methods provide a criterion for automatic extension.

Meromorphic continuation of Igusa zeta integrals yields algebraic geometric extension criteria.

The paper advances understanding of semi-invariant distributions in p-adic analysis.

Abstract

In this paper we investigate some methods on calculating the spaces of generalized semi-invariant distributions on p-adic spaces. Using homological methods, we give a criterion of automatic extension of (generalized) semi-invariant distributions. Based on the meromorphic continuations of Igusa zeta integrals, we give another criteria with purely algebraic geometric conditions, on the extension of generalized semi-invariant distributions.