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 Nizioł. 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.

14A21, 14F08, 19E08

logarithmic geometry, semi-orthogonal decompositions, K-theory

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SMSAS, University of Kent. Canterbury, Kent CT2 7NF, UK and SISSA, Via Bonomea 265, 34136 Trieste (TS), Italy

Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa (PI), Italy