Riemann–roch for real varieties

Paul Bressler*, Mikhail Kapranov, Boris Tsygan, Eric Vasserot

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations


We prove a Riemann–Roch type result for any smooth family of smooth oriented compact manifolds. It describes the class of the conjectural higher deter-minantal gerbe associated to the fibers of the family.

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Number of pages40
StatePublished - Jan 1 2009

Publication series

NameProgress in Mathematics
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X


  • Cyclic homology
  • Determinantal gerbe
  • Lie algebroid
  • Riemann–Roch

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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    Bressler, P., Kapranov, M., Tsygan, B., & Vasserot, E. (2009). Riemann–roch for real varieties. In Progress in Mathematics (pp. 125-164). (Progress in Mathematics; Vol. 269). Springer Basel. https://doi.org/10.1007/978-0-8176-4745-2_4