Christian Pierre

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The program of Langlands is studied here on the basis of: • new concepts of global class field theory related to the explicit construction of global class fields and of reciprocity laws; • the representations of the reductive algebraic groups GL(n) constituting the n-dimensional representations of the associated global Weil-Deligne groups; • a toroidal(More)
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global program based on the infinite dimensional representations of algebraic groups over adele rings. In this context, algebraic(More)
Based upon new global class field concepts leading to two-dimensional global Langlands correspondences, a modular representation of cusp forms is proposed in terms of global elliptic bisemimodules which are (truncated) Fourier series over R . As application, the conjectures of Shimura-Taniyama-Weil, Birch-Swinnerton-Dyer and Riemann are analyzed.
New fundamental mathematical structures are introduced by the triples (left semistruc-ture, right semistructure, bisemistructure) associated with the classical mathematical structures and such that the bisemistructures, resulting from the reciprocal actions of left semistruc-tures on right semistructures, are composed of bielements which are either diagonal(More)
An algebraic extended bilinear Hilbert semispace H∓ is proposed as being the natural representation space for the algebras of von Neumann. This bilinear Hilbert semispace has a well defined structure given by the representation space Repsp(GLn(Lv ×Lv)) of an algebraic general bilinear semigroup GLn(Lv ×Lv) over the product of sets of completions(More)
Part I gives algebraic basic notions necessary to generating a graded sheaf of rings from a Galois extension, i.e. essentially a specialization, called emergent, from a ring of polynomials A[x1, ..., xm] giving rise to a set of compact connected algebraic subgroups which correspond to the different sections of the sheaf of rings θ. Part II refers to the(More)
Belgium " This paper is dedicated to R. Thom who, by his enthusiasm, convinced me of the importance of the singularities and, by his patience , backed me up along my long research towards the blowups of the versal deformations , the geometries of these processes and the (strange) attractors tied up to these ". Abstract A rather complete phenomenology of the(More)
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(More)