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Annales mathématiques du Québec

, Volume 37, Issue 2, pp 129–172 | Cite as

On the non-abelian global class field theory

  • Kâzım İlhan İkedaEmail author
Original Paper
  • 157 Downloads

Abstract

Let \(K\) be a global field. The aim of this speculative paper is to discuss the possibility of constructing the non-abelian version of global class field theory of \(K\) by “glueing” the non-abelian local class field theories of \(K_\nu \) in the sense of Koch, for each \(\nu \in \mathbb{h }_K\), following Chevalley’s philosophy of idèles, and further discuss the relationship of this theory with the global reciprocity principle of Langlands.

Keywords

Restricted free products Non-abelian global and local class field theories Global and local Langlands reciprocity principles for GL(n) 

Résumé

Soit \(K\) un corps global. Le but de cet article spéculatif est d’une part de discuter de la possibilité de construire une version non abélienne de la théorie du corps de classes global de \(K\) en recollant les théories non abéliennes du corps de classes local de \(K_{\nu }\) au sens de Koch, pour tout \(\nu \in \mathbb h _K\), via la philosophie des idèles de Chevalley, et d’investiguer d’autre part le lien entre cette théorie et le principe de réciprocité globale de Langlands.

Mathematics Subject Classification

11R39 11S37 

Notes

Acknowledgments

The author would like to express his gratitude to the organizers of the Adrasan Workshop on “\(L\)-functions and Algebraic Numbers” for inviting him to deliver a lecture series on “Langlands correspondence for \(\mathrm{GL }{(n)}\)”, and the hospitality that he received during the workshop. The author would also like to thank Katsuya Miyake for his encouragment and interest in this work, where the ideas in his papers [40, 41] turned out to be central in our work, and to Ali Altuǧ for very carefully reading a preliminary version of this work and pointing out numerous inaccuracies. The author and this work were partially supported by TÜBİTAK Project No. 107T728.

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Copyright information

© Fondation Carl-Herz and Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Dept. of MathYeditepe U.IstanbulTurkey

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