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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Dedicated to the memory of José María Muñoz Porras.
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Research of José María Muñoz Porras, Fernando Pablos Romo and Francisco José Plaza Martín supported by Grant MTM2015-66760-P of MINECO and SA030G18 of JCyL. Research of Luis Manuel Navas Vicente supported by Grant MTM2015-65888-C4-4-P (MINECO/FEDER).
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Muñoz Porras, J.M., Navas Vicente, L.M., Pablos Romo, F. et al. An idelic quotient related to Weil reciprocity and the Picard group. Collect. Math. 71, 151–171 (2020). https://doi.org/10.1007/s13348-019-00252-7
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DOI: https://doi.org/10.1007/s13348-019-00252-7