On logarithmic reduction of cohomologically tame elliptic surface

TL;DR

This paper establishes cohomological criteria for logarithmic good reduction of elliptic surfaces, providing new insights into their behavior in positive characteristic and advancing understanding of log smooth morphisms.

Contribution

It introduces cohomological criteria for logarithmic good reduction of elliptic surfaces and extends results to positive characteristic and log smooth morphisms.

Findings

Cohomological criteria for logarithmic good reduction.

General results on elliptic surfaces in positive characteristic.

Insights into log smooth morphisms.

Abstract

We give cohomological criteria for logarithmic good reduction of elliptic surfaces up to modification. Along the way, we prove several more general results about such surfaces in positive characteristic, as well as about log smooth morphisms.