n-Dimensional geometric-shifted global bilinear correspondences of Langlands on mixed motives III

TL;DR

This paper advances the understanding of Langlands correspondences by exploring geometric-shifted bilinear correspondences on mixed motives, utilizing elliptic operators and spectral representations within algebraic and motivic frameworks.

Contribution

It introduces a novel approach to Langlands correspondences through geometric-shifted bilinear structures on mixed motives, connecting them with elliptic operators and spectral theory.

Findings

Development of bilinear holomorphic supercuspidal spectral representations.

Establishment of correspondence between mixed motives and algebraic semigroups.

Extension of Langlands program to geometric-shifted bilinear contexts.

Abstract

This third paper,devoted to global correspondences of Langlands,bears more particularly on geometric-shifted bilinear correspondences on mixed (bi)motives generated under the action of the products,right by left,of differential elliptic operators.The mathematical frame,underlying these correspondences,deals with the categories of the Suslin-Voevodsky mixed (bi)motives and of the Chow mixed (bi)motives which are both in one-to-one correspondence with the functional representation spaces of the shifted algebraic bilinear semigroups.A bilinear holomorphic and supercuspidal spectral representation of an elliptic bioperator is then developed.