Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes (Q2200454)

Summary: 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 \textit{K. Hagihara} [\(K\)-Theory 29, No. 2, 75--99 (2003; Zbl 1038.19002); Doc. Math. 21, 1345--1396 (2016; Zbl 1357.19001)] and \textit{W. Nizioł} [ibid. 13, 505--551 (2008; Zbl 1159.19003)]. Our techniques allow us to generalize Hagihara and Nizioł's results to a much larger class of invariants in addition to $K$-theory, and also to extend them to more general logarithmic stacks.