A plectic Taniyama group

2016/06/10 by Chris Blake, Blake, Chris · 1 citation
Mathematics · #11G15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1606.03320

openalex publication_date 2016/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit Langlands' construction of the Taniyama group to define a plectic Taniyama group for any totally real field F. The construction is functorial in F and recovers Langlands' original Taniyama group when F = Q. We relate our construction to Nekovar's 'hidden symmetries' in classical CM theory, generalising the relationship between the Taniyama group and Tate's half-transfer maps.

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• The plectic conjecture over function fields

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