2010/09/14 by Christian Pierre, Pierre, Christian
Mathematics · #11F70 #11F80 #11R39 #14D15 #14F35 #19D10 #55R45 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #General Mathematics (math.GM) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1009.2613
openalex publication_date 2010/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper revisits concretely the algebraic K-theory in the light of the global program of Langlands by taking into account the new algebraic interpretation of homotopy viewed as deformation(s) of Galois representations given by compactified algebraic groups. More concretely, we introduce higher algebraic bilinear K-theories referring to homotopy and cohomotopy and related to the reducible bilinear global program of Langlands as well as mixed higher bilinear KK-theories related to dynamical geometric bilinear global program of Langlands.