Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes
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. Our techniques allow us to generalize Hagihara and Nizio's results to a much larger class of invariants in addition to K-theory, and also to extend them to more general logarithmic stacks.
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