The Atiyah class, Hochschild cohomology and the Riemann–Roch theorem
نویسنده
چکیده
The present paper grew up from a question posed to the author by B. Feigin: ”Why does the Todd class look like the invariant volume form on a Lie group?” The answer is in a sense contained in the proof of proposition 6. In the first part we develop a formalism describing the Atiyah class, Hochschild cohomology and homology and relations between them. Essentially we introduce a global analog of Hochschild–Kostant–Rosenberg isomorphism from [9]. One may consider the Atiyah class as a morphism from the identity functor to tensoring by the cotangent bundle functor shifted by one on the derived category D(X) of coherent sheaves on a smooth manifold:
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