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# Pure and Applied Mathematics Quarterly

## Volume 11 (2015)

### Number 2

### $K$-theoretic and categorical properties of toric Deligne–Mumford stacks

Pages: 239 – 266

DOI: http://dx.doi.org/10.4310/PAMQ.2015.v11.n2.a3

#### Authors

#### 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.

#### Keywords

toric Deligne–Mumford stacks, orbifolds, $K$-theory, localization, derived category of coherent sheaves, Fourier–Mukai transformation, flop, $K$-equivalence, equivariant, variation of GIT quotient

#### 2010 Mathematics Subject Classification

Primary 14A20. Secondary 14F05, 19L47.