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A generalization of the Contou-Carrère symbol

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Abstract

Using techniques of Algebraic Geometry, the aim of this paper is to give a generalized definition of the Contou-Carrère symbol as a morphism of schemes. In fact, from formal schemes and Heisenberg groups, we provide a new definition of the Contou-Carrère symbol and a generalization of it associated with a separable extension. Moreover, a reciprocity law is proved and classical explicit reciprocity laws are recovered from it.

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Authors and Affiliations

  1. Department de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008, Salamanca, Spain

    Fernando Pablos Romo

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  1. Fernando Pablos Romo
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Correspondence to Fernando Pablos Romo.

Additional information

This work is partially supported by the DGESYC research contract n. BFM2003-00078 and Castilla y León Regional Government contract SA064/01.

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Romo, F.P. A generalization of the Contou-Carrère symbol. Isr. J. Math. 141, 39–60 (2004). https://doi.org/10.1007/BF02772210

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  • DOI: https://doi.org/10.1007/BF02772210

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