On a good reduction criterion for proper polycurves with sections

TL;DR

This paper establishes a new good reduction criterion for proper polycurves with sections, extending the classical criterion for hyperbolic curves to higher dimensions under mild assumptions.

Contribution

It introduces a higher dimensional good reduction criterion for proper polycurves with sections, generalizing previous results for hyperbolic curves.

Findings

Provides a criterion for good reduction of polycurves with sections

Extends classical hyperbolic curve reduction criteria to higher dimensions

Operates under mild assumptions for broader applicability

Abstract

We give a good reduction criterion for proper polycurves with sections,i.e., successive extensions of family of curves with section, under mild assumption. This criterion is a higher dimensional version of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa.