Criteria for good reduction of proper polycurves

TL;DR

This paper establishes criteria for determining when hyperbolic polycurves, composed of successive curve extensions, have good reduction properties, extending known results from hyperbolic curves to higher dimensions.

Contribution

It provides higher-dimensional good reduction criteria for hyperbolic polycurves, generalizing the classical criteria for hyperbolic curves by Oda and Tamagawa.

Findings

Established new reduction criteria for hyperbolic polycurves

Extended classical curve reduction results to higher dimensions

Provided conditions under mild assumptions for good reduction

Abstract

We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under mild assumption. These criteria are higher dimensional version of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa.