GL(2)-structures of the Langlands global program

TL;DR

This paper explores the structure of the Langlands program through the lens of GL(2)-structures, analyzing how singularities and their deformations influence the associated functional representation spaces and correspondences.

Contribution

It introduces a novel geometric framework using universal GL(2)-structures and singularity theory to understand Langlands correspondences.

Findings

Singularities lead to new covering representation spaces.

Deformations and blowups relate to Langlands correspondences.

Universal GL(2)-structures unify various cases.

Abstract

All kinds of global correspondences of Langlands are evaluated from the functional representation spaces of the algebraic bilinear semigroups GL2(.x.) with entries in products,right by left,of sets of archimedean increasing completions. Degenerate singularities on these functional representation spaces can give rise,by versal deformations and blowups of these,to one or two new covering functional representation spaces of GL2(.x.) according to the type of considered singularities. The discovered correspondences of Langlands are associated with singular and nonsingular universal GL(2)-structures.