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The Atiyah class, Hochschild cohomology and the Riemann–Roch theorem
Author(s) -
Markarian Nikita
Publication year - 2009
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn064
Subject(s) - mathematics , cohomology , formalism (music) , pure mathematics , characteristic class , class (philosophy) , algebra over a field , topology (electrical circuits) , computer science , combinatorics , artificial intelligence , art , musical , visual arts
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.