Mattia Talpo: Kummer-étale additive invariants of log schemes

Hagihara and Nizioł proved decomposition results for the Kummer-étale (and -flat) algebraic K-theory of some class of nice log schemes, in terms of the algebraic K-theory of the strata of the “boundary”. I will talk about some work with Sarah Scherotzke and Nicolò Sibilla about a categorification (at the level of non-commutative motives) of this decomposition. I will start by recalling some basics on log schemes, then move on to root stacks and semi-orthogonal decompositions of their derived categories, which are the main tools of our work, and to describing our results.