Semistable sheaves and comparison isomorphisms in the semistable case

TL;DR

This paper develops a framework for semistable etale sheaves on smooth proper schemes with semistable reduction over local fields, establishing comparison isomorphisms in this context.

Contribution

It introduces the category of semistable etale sheaves and proves semistable comparison isomorphisms under specific hypotheses.

Findings

Defined the category of semistable etale sheaves.

Proved semistable comparison isomorphisms.

Applicable to schemes with semistable reduction.

Abstract

For a smooth proper scheme over a local field of mixed characteristics which has semistable reduction we define the category of its semistable etale sheaves and under certain hypothesis we prove the appropriate semistable comparison isomorphisms.