An algebraic approach to the existence of valuative interpolation

TL;DR

This paper introduces an algebraic method using the asymptotic Samuel function to determine the existence of valuative interpolation, generalizing previous complex analytic characterizations and extending to infinite cases.

Contribution

It provides a novel algebraic framework for valuative interpolation, broadening the scope of prior complex analytic results and including infinite interpolation scenarios.

Findings

Characterization of valuative interpolation via asymptotic Samuel function

Extension of interpolation existence criteria to infinite cases

Generalization of complex analytic results to algebraic setting

Abstract

An algebraic approach is presented for the valuative interpolation problem, which recovers and generalizes prior characterizations known in the complex analytic setting by the authors. We use the asymptotic Samuel function to give the characterization of the existence of valuative interpolation. We also give a characterization of the existence in the infinite valuative interpolation problem.