000			02128 a2200241 4500
999			_c54422 _d54422
008			210324b ||||| |||| 00| 0 eng d
020			_a9780521172745
082			_a512.42 _bLAU
100			_aLaumon, Gérard
245			_aCohomology of drinfeld modular varieties: part 1. geometry, counting of points and local harmonic analysis
260			_bCambridge University Press, _c2010. _aCambridge:
300			_axiii, 344p. : ill. ; _bpb, _c23 cm.
365			_aGBP _b44.00
440			_a Cambridge studies in advanced mathematics ; 41
504			_aIncludes index and bibliographical references.
520			_aCohomology of Drinfeld Modular Varieties provides an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. This second volume is concerned with the Arthur-Selberg trace formula, and with the proof in some cases of the Rmamanujan-Petersson conjecture and the global Langlands conjecture for function fields. It is based on graduate courses taught by the author, who uses techniques which are extensions of those used to study Shimura varieties. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated. Several appendices on background material keep the work reasonably self-contained. It is the first book on this subject and will be of much interest to all researchers in algebraic number theory and representation theory.
650			_aHomology theory
650			_aDrinfeld modular varieties
650			_aModular varieties
650			_aGeometry
650			_aLocal harmonic analysis
942			_2ddc _cTD