An idelic quotient related to Weil reciprocity and the Picard group

• José María Muñoz Porras ^[1] ; Luis Manuel Navas Vicente ^[1] ; Fernando Pablos Romo ^[1] ; Francisco José Plaza Martín ^[1]
  1. [1] Universidad de Salamanca

     Universidad de Salamanca

     Salamanca, España

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 1, 2020, págs. 151-171
• Idioma: inglés
• DOI: 10.1007/s13348-019-00252-7
• Texto completo no disponible (Saber más ...)
• Resumen

  • This paper studies the function field of an algebraic curve over an arbitrary perfect field by using the Weil reciprocity law and topologies on the adele ring. A topological subgroup of the idele class group is introduced and it is shown how it encodes arithmetic properties of the base field and of the Picard group of the curve. These results are applied to study extensions of the function field.