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