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Article overview
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Gaps in Hochschild cohomology imply smoothness for commutative algebras | Luchezar Avramov
; Srikanth Iyengar
; | Date: |
13 Dec 2004 | Subject: | Commutative Algebra; Rings and Algebras MSC-class: 13D03; 14B25. Secondary: 14M10; 16E40 | math.AC math.RA | Abstract: | The paper concerns Hochschild cohomology of a commutative algebra S, which is essentially of finite type over a commutative noetherian ring K and projective as a K-module, with coefficients in an S-module M. It is proved that vanishing of HH^n(S|K,M) in sufficiently long intervals imply the smoothness of S_q over K for all prime ideals q in the support of M. In particular, S is smooth if HH^n(S|K,S)=0 for (dim S+2) consecutive non-negative integers n. | Source: | arXiv, math.AC/0412259 | Services: | Forum | Review | PDF | Favorites |
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