JournalsdmVol. 25pp. 955–1009

Parabolic Semi-Orthogonal Decompositions and Kummer Flat Invariants of Log Schemes

  • Sarah Scherotzke

    Université du Luxembourg, Maison du Nombre 6, Avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg

  • Nicolò Sibilla

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

  • Mattia Talpo

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

Cite this article

Sarah Scherotzke, Nicolò Sibilla, Mattia Talpo, Parabolic Semi-Orthogonal Decompositions and Kummer Flat Invariants of Log Schemes. Doc. Math. 25 (2020), pp. 955–1009

DOI 10.4171/DM/768