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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1998
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/171370 |
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I19-R120-10915-1713702024-10-10T20:10:40Z http://sedici.unlp.edu.ar/handle/10915/171370 Infinitesimal K-theory : Notas de Matemática, 65 Cortiñas, Guillermo Horacio 1998 2024-10-10T17:16:08Z en Matemática 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. Material digitalizado en SEDICI gracias a la colaboración de la Biblioteca del Departamento de Matemática de la Facultad de Ciencias Exactas (UNLP). Facultad de Ciencias Exactas Publicacion seriada Publicacion seriada http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf |
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Universidad Nacional de La Plata |
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I-19 |
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R-120 |
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SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática |
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Matemática Cortiñas, Guillermo Horacio Infinitesimal K-theory : Notas de Matemática, 65 |
| topic_facet |
Matemática |
| description |
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. |
| format |
Publicacion seriada Publicacion seriada |
| author |
Cortiñas, Guillermo Horacio |
| author_facet |
Cortiñas, Guillermo Horacio |
| author_sort |
Cortiñas, Guillermo Horacio |
| title |
Infinitesimal K-theory : Notas de Matemática, 65 |
| title_short |
Infinitesimal K-theory : Notas de Matemática, 65 |
| title_full |
Infinitesimal K-theory : Notas de Matemática, 65 |
| title_fullStr |
Infinitesimal K-theory : Notas de Matemática, 65 |
| title_full_unstemmed |
Infinitesimal K-theory : Notas de Matemática, 65 |
| title_sort |
infinitesimal k-theory : notas de matemática, 65 |
| publishDate |
1998 |
| url |
http://sedici.unlp.edu.ar/handle/10915/171370 |
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AT cortinasguillermohoracio infinitesimalktheorynotasdematematica65 |
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1826544371416170496 |