2004/07/05 by Jean-Francois Dat, Dat, Jean-Francois
Mathematics · #11S37 #14G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.AG #math.NT #math.RT #msc:11S37 #msc:14G35
paper · pdf · doi:10.48550/arxiv.math/0407055
french, 120 pages
arxiv created 2004/07/05 · arxiv updated 2009/12/01
The conjecture stated by Carayol in [\em Non-abelian Lubin-Tate theory. Automorphic forms, Shimura varieties and L-functions, vol II: 15--39, Academic Press,1990] predicted that the \em supercuspidal part of the l-adic cohomology of the moduli spaces classifying certain formal groups introduced by Drinfeld would provide a simultaneaous "realization" of Langlands and Jacquet-Langlands local correspondences for \em supercuspidal representations of GLd. By works of Harris, Boyer, Harris-Taylor and Hausberger, this conjecture is now proved. On another hand, recent works by Boyer and Faltings provide a description of all the cohomology spaces and show in particular that these spaces do not retain enough information for Langlands correspondence of non-supercupidal representations. From these works, our main aim is to show how one can still get a simultaneous realization for \em elliptic representations of GLd, using the formalism of derived categories. More specifically, we describe the action of the monodromy on the (suitably defined) cohomology complex of the Drinfeld tower and get the lacking information back from this description..