An idelic quotient related to Weil reciprocity and the Picard group

  1. José María Muñoz Porras 1
  2. Luis Manuel Navas Vicente 1
  3. Fernando Pablos Romo 1
  4. Francisco José Plaza Martín 1
  1. 1 Departamento de Matemáticas and IUFFYM, Universidad de Salamanca
Journal:
Collectanea mathematica

ISSN: 0010-0757

Year of publication: 2020

Volume: 71

Fascicle: 1

Pages: 151-171

Type: Article

DOI: 10.1007/S13348-019-00252-7 DIALNET GOOGLE SCHOLAR

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Abstract

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.

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