Artículo
Abstract:
The title refers to the nilcommutative of NC-schemes introduced by M. Kapranov in 'Noncommutative Geometry Based on Commutator Expansions', J. Reine Angew. Math 505 (1998) 73-118. The latter are noncommutative nilpotent thickenings of commutative schemes. We also consider the parallel theory of nil-Poisson of NP-schemes, which are nilpotent thickenings of commutative schemes in the category of Poisson schemes. We study several variants of de Rham cohomology for NC- and NP-schemes. The variants include nilcommutative and nil-Poisson versions of the de Rham complex as well as of the cohomology of the infinitesimal site introduced by Grothendieck in Crystals and the de Rham Cohomology of Schemes, Dix exposés sur la cohomologie des schémas, Masson, Paris (1968), pp. 306-358. It turns out that each of these noncommutative variants admits a kind of Hodge decomposition which allows one to express the cohomology groups of a noncommutative scheme Y as a sum of copies of the usual (de Rham, infinitesimal) cohomology groups of the underlying commutative scheme X (Theorems 6.1, 6.4, 6.7). As a byproduct we obtain new proofs for classical results of Grothendieck (Corollary 6.2) and of Feigin and Tsygan (Corollary 6.8) on the relation between de Rham and infinitesimal cohomology and between the latter and periodic cyclic homology.
Registro:
| Documento: | Artículo |
| Título: | De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry |
| Autor: | Cortiñas, G. |
| Filiación: | Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina |
| Palabras clave: | Commutator filtration; Cyclic homology; Grothendieck topology |
| Año: | 2003 |
| Volumen: | 136 |
| Número: | 2 |
| Página de inicio: | 171 |
| Página de fin: | 208 |
| DOI: | http://dx.doi.org/10.1023/A:1022732008165 |
| Título revista: | Compositio Mathematica |
| Título revista abreviado: | Compos. Math. |
| ISSN: | 0010437X |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0010437X_v136_n2_p171_Cortinas.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0010437X_v136_n2_p171_Cortinas |
Referencias:
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Citas:
---------- APA ----------
(2003) . De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry. Compositio Mathematica, 136(2), 171-208.http://dx.doi.org/10.1023/A:1022732008165
---------- CHICAGO ----------
Cortiñas, G. "De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry" . Compositio Mathematica 136, no. 2 (2003) : 171-208.http://dx.doi.org/10.1023/A:1022732008165
---------- MLA ----------
Cortiñas, G. "De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry" . Compositio Mathematica, vol. 136, no. 2, 2003, pp. 171-208.http://dx.doi.org/10.1023/A:1022732008165
---------- VANCOUVER ----------
Cortiñas, G. De Rham and Infinitesimal Cohomology in Kapranov's Model for Noncommutative Algebraic Geometry. Compos. Math. 2003;136(2):171-208.http://dx.doi.org/10.1023/A:1022732008165
