# Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes

@article{Scherotzke2018ParabolicSD, title={Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes}, author={Sarah Scherotzke and Nicol{\`o} Sibilla and Mattia Talpo}, journal={arXiv: Algebraic Geometry}, year={2018} }

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{\l}. Our techniques allow us to generalize Hagihara and Nizio{\l}'s results to a much larger class of invariants in addition to K-theory, and also to extend them to more general logarithmic stacks.

## One Citation

## References

SHOWING 1-10 OF 51 REFERENCES

Geometricity for derived categories of algebraic stacks

- Mathematics
- 2016

We prove that the dg category of perfect complexes on a smooth, proper Deligne–Mumford stack over a field of characteristic zero is geometric in the sense of Orlov, and in particular smooth and…

Moduli of parabolic sheaves on a polarized logarithmic scheme

- Mathematics
- 2014

We generalize the construction of moduli spaces of parabolic sheaves given by Maruyama and Yokogawa in [MY92] to the case of a projective fine saturated log scheme with a fixed global chart.…

Parabolic sheaves with real weights as sheaves on the Kato–Nakayama space

- MathematicsAdvances in Mathematics
- 2018

On a logarithmic version of the derived McKay correspondence

- MathematicsCompositio Mathematica
- 2018

We globalize the derived version of the McKay correspondence of Bridgeland, King and Reid, proven by Kawamata in the case of abelian quotient singularities, to certain logarithmic algebraic stacks…

Structure Theorem of Kummer Etale K-Group II

- Mathematics
- 2016

In this article, we investigate the lambda-ring structure of Kummer etale K-groups for some class of logarithmic schemes, up to torsion. In particular, we give a logarithmic analogue of Chow groups…

Smooth toric Deligne-Mumford stacks

- Mathematics
- 2010

Abstract We give a geometric definition of smooth toric Deligne-Mumford stacks using the action of a “torus”. We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms…

A relation between the parabolic Chern characters of the de Rham bundles

- Mathematics
- 2006

In this paper, we consider the weight i de Rham–Gauss–Manin bundles on a smooth variety arising from a smooth projective morphism $${f:X_U\longrightarrow U}$$ for $${i\geq 0}$$ . We associate to each…

Atiyah-Segal theorem for Deligne-Mumford stacks and applications

- MathematicsJournal of Algebraic Geometry
- 2020

We prove an Atiyah-Segal isomorphism for the higher
K
K
-theory of coherent sheaves on quotient Deligne-Mumford stacks over
C
\mathbb {C}
. As an application, we prove the…

Infinite root stacks and quasi‐coherent sheaves on logarithmic schemes

- Mathematics
- 2014

We define and study infinite root stacks of fine and saturated logarithmic schemes, a limit version of the root stacks introduced by Niels Borne and the second author in Adv. Math. (231 (2012)…