Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes

TL;DR

This paper develops semi-orthogonal decompositions for categories of parabolic sheaves on log schemes, generalizing Kummer flat K-theory results to broader invariants and stacks.

Contribution

It introduces a new categorical framework for decomposing parabolic sheaves on log schemes, extending existing K-theory results to more invariants and stacks.

Findings

Constructed semi-orthogonal decompositions for parabolic sheaves.

Categorified Kummer flat K-theory decomposition theorems.

Extended results to a larger class of invariants and stacks.

Abstract

We construct semi-orthogonal decompositions on triangulated categories of parabolic sheaves on certain kinds of logarithmic schemes. This provides a categorification of the decomposition theorems in Kummer flat K-theory due to Hagihara and Nizio{\l}. Our techniques allow us to generalize Hagihara and Nizio{\l}'s results to a much larger class of invariants in addition to K-theory, and also to extend them to more general logarithmic stacks.