A Note on Steinberg Symbols on Algebraic Curves
[EN]The aim of this paper is to provide a method for defining Steinberg symbols on a complete algebraic curve over a perfect field k from the commutator of a certain extension of groups. This extension is associated with a group morphism ϕ : k* → G. With this definition the reciprocity law is a cons...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2003 |
| País: | España |
| Institución: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/164049 |
| Acceso en línea: | http://hdl.handle.net/10366/164049 |
| Access Level: | acceso embargado |
| Palabra clave: | Steinberg symbol Algebraic curve Reciprocity law 12 Matemáticas 1201 Álgebra |
| Sumario: | [EN]The aim of this paper is to provide a method for defining Steinberg symbols on a complete algebraic curve over a perfect field k from the commutator of a certain extension of groups. This extension is associated with a group morphism ϕ : k* → G. With this definition the reciprocity law is a consequence of the finiteness of the cohomology groups H^0(C, _C ) and H^1(C, _C ). Using this method, Hilbert's norm residue symbol on an algebraic curve and the symbol (a, b)_v for the field ℚ_p (n = 2) can be defined. |
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