Basic finite \'etale equivalence relations

TL;DR

This paper characterizes quotients of non-degenerate abelian fibrations by finite étale equivalence relations and explores their degenerations, revealing that non-uniruled degenerations tend to be almost non-degenerate.

Contribution

It provides a new characterization of quotients of abelian fibrations under finite étale equivalence relations and analyzes their degeneration behavior.

Findings

Quotients of abelian fibrations by finite étale relations are characterized.

Degenerations of these quotients tend to be almost non-degenerate if non-uniruled.

The work advances understanding of the structure and degeneration of abelian fibrations.

Abstract

We characterize quotient of a non-degenerate abelian fibration by a finite \'etale equivalence relation. We show that non-uniruled degenerations of each such quotient tend to be almost non-degenerate.