The Continuous Hochschild Cochain Complex of a Scheme
| dc.creator | Yekutieli, Amnon | |
| dc.date | 2001-11-08 | |
| dc.date.accessioned | 2026-07-07T04:44:27Z | |
| dc.date.available | 2026-07-07T04:44:27Z | |
| dc.description | Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we assign the complex Hom^{cont}_X(C(X),M) of continuous Hochschild cochains with values in M. Our first main result is that when X is smooth over K there is a functorial isomorphism between the complex of continuous Hochschild cochains and RHom_{X2}(O_X,M), in the derived category D(Mod(O_{X2})). The second main result is that if X is smooth of relative dimension n and n! is invertible in K, then the standard map from Hochschild chains to differential forms induces a decomposition of Hom^{cont}_X(C(X),M) in derived category D(Mod(O_X)). When M = O_X this is the precisely the quasi-isomorphism underlying the Kontsevich Formality Theorem. Combining the two results above we deduce a decomposition of the global Hochschild cohomology with values in M. | |
| dc.description | 16 pages, AMSLaTeX, replaces math.AG/0005127 | |
| dc.identifier | https://arxiv.org/abs/math/0111094 | |
| dc.identifier | http://arxiv.org/abs/math/0111094 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62596 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Primary 16E40; Secondary 14F10, 18G10, 13H10 | |
| dc.title | The Continuous Hochschild Cochain Complex of a Scheme | |
| dc.type | text |