TL;DR
This paper generalizes Langlands' Taniyama group to totally real fields, introducing a plectic version that is functorial and relates to classical CM theory and Nekovar's hidden symmetries.
Contribution
It constructs a functorial plectic Taniyama group for any totally real field, extending Langlands' original framework and connecting to advanced CM theory concepts.
Findings
Defines a plectic Taniyama group for totally real fields.
Recovers Langlands' Taniyama group over Q.
Links to Nekovar's hidden symmetries in CM theory.
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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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology