A Note on Semilocal Reciprocity Laws on Curves |
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Authors: | Yolanda África Zárate Herrera |
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Affiliation: | 1. Departmento de Matemáticas , Universidad de Salamanca , Salamanca, Espa?a yzarate@mukai.usal.es yazarate@yahoo.es |
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Abstract: | The aim of this work is to offer a definition of the Contou-Carrère symbol associated with a closed point of an algebraic curve and with a local ring of dimension zero, first, and then with a semilocal ring of dimension zero, from the commutator of a certain central extension. When the curve is complete, we deduce the reciprocity law in both cases. Moreover, we give some applications to the residues, and obtain explicit relations between the classic residue and the Witt residue. Communicated by C. Pedrini. |
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Keywords: | Algebraic curves Contou-Carrère symbol Reciprocity law Semilocal ring |
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