2006/06/14 by Christian Pierre, Pierre, Christian · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #math.RT
paper · pdf · doi:10.48550/arxiv.math/0606342
117 pages
arxiv created 2006/06/14 · arxiv updated 2009/12/01
A rather complete phenomenology of the singularities is developed according to a new algebraic point of view in the frame of Langlands global correspondences. That is to say,a process of: -singularizations and versal deformations of these, -singularizations and monodromies of these, is envisaged on all the sections of sheaves of differentiable (bi)functions on (bi)linear algebraic (semi)groups constituting the n-dimensional representations of the global Weil groups. To get the searched holomorphic and cuspidal representations,it is necessary to consider: -the resolutions of the singularities and the blowups of the versal deformations; -the resolutions of the singularities in the monodromy cases. Furthermore, the geometry of the versal deformations and of their blowups is studied, as well as the associated dynamics leading to the consideration of singular hyperbolic attractors and of singular strange attractors.