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On the $$K$$-theory of smooth toric DM stacks. (English) Zbl 1171.14301
Becker, Katrin (ed.) et al., Snowbird lectures on string geometry. Proceedings of an AMS-IMS-SIAM joint summer research conference on string geometry, June 5–11, 2004, Snowbird, UT, USA. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3663-3/pbk). Contemporary Mathematics 401, 21-42 (2006).
Summary: We explicitly calculate the Grothendieck $$K$$-theory ring of a smooth toric Deligne-Mumford stack and define an analog of the Chern character. In addition, we calculate $$K$$-theory pushforwards and pullbacks for weighted blowups of reduced smooth toric Deligne-Mumford stacks.
For the entire collection see [Zbl 1088.81008].

##### MSC:
 14C35 Applications of methods of algebraic $$K$$-theory in algebraic geometry 14A20 Generalizations (algebraic spaces, stacks) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies 19E20 Relations of $$K$$-theory with cohomology theories
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