Infinitesimal K-theory : Notas de Matemática, 65
In section 1 we develop the language of categories with deformations. In section 2 we construct the localization C —> C[Def-1] for a category with deformations. A general criterion for the existence of derived functors with respect to this localization is established in section 3. In section...
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| Formato: | Publicacion seriada |
| Lenguaje: | Inglés |
| Publicado: |
1998
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/171370 |
| Aporte de: |
| Sumario: | In section 1 we develop the language of categories with deformations. In section 2 we construct the localization C —> C[Def-1] for a category with deformations. A general criterion for the existence of derived functors with respect to this localization is established in section 3. In section 4 we show that both non-commutative de Rham cohomology and the rational 4—construction of the elementary group meet this criterion, and compute their derived functors. The sheaf theoretic approach is developed in section 5 where the character cr mentioned above is constructed. The isomorphism (6) is proven in section 6. Also in this section we conjecture that Hn(A, K®) = 0 for positive n, and show that this conjecture is related to finding a non commutative analogue of Grothendieck’s isomorphism (4). The map (1) is constructed in section 7; a more concrete interpretation of Free'nf as a category of integrable connections with as maps the gauge transformations is discussed. |
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