K-Theoretic and Categorical Properties of Toric Deligne--Mumford Stacks

Abstract

We prove the following results for toric Deligne-Mumford stacks, under minimal compactness hypotheses: the Localization Theorem in equivariant K-theory; the equivariant Hirzebruch-Riemann-Roch theorem; the Fourier--Mukai transformation associated to a crepant toric wall-crossing gives an equivariant derived equivalence.

14 pages, no figures. v2: references updated, v3: minor revision, final version

References in corpus (3)

• Log Crepant Birational Maps and Derived Categories
• The Crepant Transformation Conjecture for Toric Complete Intersections
• Riemann-Roch for Deligne-Mumford stacks

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• The Crepant Transformation Conjecture implies the Monodromy Conjecture
• Crepant Transformation Correspondence For Toric Stack Bundles
• Note on the Bondal-Orlov Functors for Toric DM Stacks