Vol. 6, No. 3, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Author Index
To Appear
 
Other MSP Journals
$K\mkern-2mu$-theory and the singularity category of quotient singularities

Nebojsa Pavic and Evgeny Shinder

Vol. 6 (2021), No. 3, 381–424
Abstract

We study Schlichting’s K-theory groups of the Buchweitz–Orlov singularity category 𝒟sg(X) of a quasiprojective algebraic scheme Xk with applications to algebraic K-theory.

We prove for isolated quotient singularities over an algebraically closed field of characteristic zero that K0(𝒟sg(X)) is finite torsion, and that K1(𝒟sg(X)) = 0. One of the main applications is that algebraic varieties with isolated quotient singularities satisfy rational Poincaré duality on the level of the Grothendieck group; this allows computing the Grothendieck group of such varieties in terms of their resolution of singularities. Other applications concern the Grothendieck group of perfect complexes supported at a singular point and topological filtration on the Grothendieck groups.

Keywords
$K\mkern-2mu$-theory of singular varieties, quotient singularity, derived category, singularity category
Mathematical Subject Classification 2010
Primary: 14J17, 18E30, 19E08
Milestones
Received: 29 March 2019
Revised: 10 November 2020
Accepted: 6 December 2020
Published: 11 September 2021
Authors
Nebojsa Pavic
Leibniz Universität Hannover
Hannover
Germany
Evgeny Shinder
School of Mathematics and Statistics
University of Sheffield
Sheffield
United Kingdom
National Research University Higher School of Economics
Moscow
Russia