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.
Categories: math.AG