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Chern character for twisted complexes. (English) Zbl 1146.19003

Kapranov, Mikhail (ed.) et al., Geometry and dynamics of groups and spaces. In memory of Alexander Reznikov. Partly based on the international conference on geometry and dynamics of groups and spaces in memory of Alexander Reznikov, Bonn, Germany, September 22–29, 2006. Basel: Birkhäuser (ISBN 978-3-7643-8607-8/hbk). Progress in Mathematics 265, 309-324 (2008).
Summary: We construct the Chern character from the \(K\)-theory of twisted perfect complexes of an algebroid stack to the negative cyclic homology of the algebra of twisted matrices associated to the stack.
For the entire collection see [Zbl 1130.00014].

MSC:

19E99 \(K\)-theory in geometry
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
18G35 Chain complexes (category-theoretic aspects), dg categories
14A20 Generalizations (algebraic spaces, stacks)
19D55 \(K\)-theory and homology; cyclic homology and cohomology
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