On a logarithmic version of the derived McKay correspondence

Abstract

We globalize the derived version of the McKay correspondence of Bridgeland-King-Reid, proven by Kawamata in the case of abelian quotient singularities, to certain log algebraic stacks with locally free log structure. The two sides of the correspondence are given respectively by the infinite root stack and by a certain version of the valuativization (the projective limit of every possible log blow-up). Our results imply, in particular, that in good cases the category of coherent parabolic sheaves with rational weights is invariant under log blow-up, up to Morita equivalence.

v3: Implemented referee's suggestions. 55 pages. Final version, to appear in Compositio Mathematica

References in corpus (3)

• Infinite root stacks and quasi-coherent sheaves on logarithmic schemes
• Boundedness of the space of stable logarithmic maps
• Kato-Nakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes

Cited by in corpus (2)

• The Log Product Formula in quantum $K$-theory
• Gluing semi-orthogonal decompositions