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- W2075052117 abstract "Let $X$ be a smooth scheme over a field of characteristic 0. Let $dd^{bullet}(X)$ be the complex of polydifferential operators on $X$ equipped with Hochschild co-boundary. Let $L(dd^1(X))$ be the free Lie algebra generated over $strc$ by $dd^1(X)$ concentrated in degree 1 equipped with Hochschild co-boundary. We have a symmetrization map $I: oplus_k sss^k(L(dd^1(X))) rar dd^{bullet}(X)$. Theorem 1 of this paper measures how the map $I$ fails to commute with multiplication. A consequence of Theorem 1 and Theorem 2 is Corollary 1, a result dual to Theorem 1 of Markarian [3] that measures how the Hochschild-Kostant-Rosenberg quasi-isomorphism fails to commute with multiplication. In order to understand Theorem 1 conceptually, we prove a theorem (Theorem 3) stating that $dd^{bullet}(X)$ is the universal enveloping algebra of in $dcat$. An easy consequence of Theorem 3 is Theorem 4, which interprets the Chern $E$ as the character of the representation $E$ of $T_X[-1]$ and gives a description of the big Chern classes of $E$. Finally, Theorem 4 along with Theorem 1 is used to give an explicit formula (Theorem 5) expressing the big Chern classes of $E$ in terms of the components of the Chern of $E$." @default.
- W2075052117 created "2016-06-24" @default.
- W2075052117 creator A5074631616 @default.
- W2075052117 date "2005-12-05" @default.
- W2075052117 modified "2023-09-27" @default.
- W2075052117 title "The big Chern classes and the Chern character" @default.
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