The Atiyah class, Hochschild cohomology and the Riemann-Roch theorem

2006/10/31 by Nikita Markarian · 2 citations
Mathematics · #Advanced Operator Algebra Research #Algebra over a field #Chain (unit) #Cohomology #Formalism (music) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Sheaf cohomology #math.AG

paper · pdf · doi:10.1112/jlms/jdn064

16 pages; added references, corrected typos and removed irrelevant passages

arxiv created 2008/09/22 · openalex publication_date 2008/10/09 · arxiv updated 2014/02/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We develop a formalism involving Atiyah classes of sheaves on a smooth manifold, Hochschild chain and cochain complexes. As an application we prove a version of the Riemann–Roch theorem.

Cited by

• From Atiyah Classes to Homotopy Leibniz Algebras
• Derived category [wikipedia]