Weil Reciprocity Law and the Theorem of Residues

2019/05/28 by José M. Muñoz Porras, Porras, José M. Muñoz, Francisco J. Plaza Martín +1
Mathematics · #11R37 #14H05 #19F15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:11R37 #msc:14H05 #msc:19F15

paper · pdf · doi:10.48550/arxiv.1905.11774

arxiv created 2019/05/28 · openalex publication_date 2019/05/28 · arxiv updated 2019/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper shows how the Theorem of Residues (TR) and the Gelfand-Fuchs cocycle can be deduced in a simple way from the Weil Reciprocity Law (WRL). Indeed, if one understand WRL as the triviality of certain extension of groups, then TR is the same statement at the level of Lie algebras. Finally, the Gelfand-Fuchs cocycle can also be obtained in this way.

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