Algebraic K-theory of singularity categories of quotient singularities

Evgeny Shinder (University of Sheffield)

Wednesday 12th September, 2018 16:00-17:00 Maths 311B

Abstract

In this joint work in progress with Nebojsa Pavic, we study Schlichting K-groups of the Buchweitz-Orlov singularity category. After developing the basic techniques, we concentrate on the case of isolated quotient singularities, where we prove that K_0 of the singularity category is finite torsion and that its K_1 is zero. This has nontrivial applications to the Grothendieck groups K_0(X) and K_0(X on Sing(X)) for isolated quotient singularities. In particular we compute K_0 of weighted projective spaces with coprime weights and prove an old conjecture of Srinivas on perfect complexes concentrated at the singular locus.

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