Parabolic sheaves on logarithmic schemes

TL;DR

This paper establishes a new framework for understanding parabolic sheaves using logarithmic geometry, reformulating logarithmic structures via symmetric monoidal categories and relating sheaves to stacks of roots.

Contribution

It introduces a novel interpretation of parabolic sheaves as quasi-coherent sheaves on stacks of roots within logarithmic geometry, with a reformulation of logarithmic structures.

Findings

Parabolic sheaves are interpreted as quasi-coherent sheaves on stacks of roots.

Logarithmic structures are reformulated using symmetric monoidal categories.

The approach provides a new perspective on the geometry of parabolic sheaves.

Abstract

We show how the natural context for the definition of parabolic sheaves on a scheme is that of logarithmic geometry. The key point is a reformulation of the concept of logarithmic structure in the language of symmetric monoidal categories, which might be of independent interest. Our main result states that parabolic sheaves can be interpreted as quasi-coherent sheaves on certain stacks of roots.