3-Cocycles, symbols and reciprocity laws on curves
[EN]We introduce a new approach for the study of two-dimensional symbols, F^∗ ×F^∗ ×F^∗ → G, where F is a discrete valuation field and G is a commutative group. From central extensions of groups we obtain a three-cocycle {·, ·, ·} and the symbol is a differentiated element of the cohomology class [{...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2006 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/164060 |
| Acceso en línea: | http://hdl.handle.net/10366/164060 |
| Access Level: | acceso abierto |
| Palabra clave: | 3-cocycle Arithmetic symbols Reciprocity laws 12 Matemáticas |
| Sumario: | [EN]We introduce a new approach for the study of two-dimensional symbols, F^∗ ×F^∗ ×F^∗ → G, where F is a discrete valuation field and G is a commutative group. From central extensions of groups we obtain a three-cocycle {·, ·, ·} and the symbol is a differentiated element of the cohomology class [{·, ·, ·}] ∈ H^3(F^∗,G). Our construction generalizes well-known two-dimensional symbols, such as the Parshin symbol on a surface, and we offer a proof and a conjecture for reciprocity laws on curves related to these symbols. |
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