On Jacquet–Langlands isogeny over function fields
نویسنده
چکیده
Article history: Received 15 August 2010 Revised 31 December 2010 Accepted 3 January 2011 Available online xxxx Communicated by David Goss MSC: primary 11G18, 11G09 secondary 14H40
منابع مشابه
The Eisenstein Ideal and Jacquet-Langlands Isogeny over Function Fields
Let p and q be two distinct prime ideals of Fq[T ]. We use the Eisenstein ideal of the Hecke algebra of the Drinfeld modular curveX0(pq) to compare the rational torsion subgroup of the Jacobian J0(pq) with its subgroup generated by the cuspidal divisors, and to produce explicit examples of Jacquet-Langlands isogenies. Our results are stronger than what is currently known about the analogues of ...
متن کاملOn Classification of Some Classes of Irreducible Representations of Classical Groups
Introduction 2 1. Harmonic analysis and unitary duals 2 2. Non-discrete locally compact fields, classical groups, reductive groups 4 3. K0-finite vectors 7 4. Smooth representations 8 5. Parabolically induced representations 9 6. Jacquet modules 12 7. Filtrations of Jacquet modules 14 8. Square integrable and tempered representations 15 9. Langlands classification 16 10. Geometric lemma and alg...
متن کاملSome Endoscopic Properties of The Essentially Tame Jacquet-Langlands Correspondence
Let F be a non-Archimedean local field of characteristic 0 and G be an inner form of the general linear group G = GLn over F . We show that the rectifying character appearing in the essentially tame Jacquet-Langlands correspondence of Bushnell and Henniart for G and G can be factorized into a product of some special characters, called zeta-data in this paper, in the theory of endoscopy of Langl...
متن کاملA Rank Inequality for the Tate Conjecture over Global Function Fields
We present an observation of D. Ramakrishnan concerning the Tate Conjecture for varieties over a global function field (i.e., the function field of a smooth projecture curve over a finite field), which was pointed out during a lecture given at the AIM’s workshop on the Tate Conjecture in July 2007. The result is perhaps “known to the experts,” but we record it here, as it does not appear to be ...
متن کاملLecture 16: Review of representation theory
• The theory of admissible representations of GL(2,Qp) (or more generally, GL(2, F ) with F/Qp a finite extension). • The theory of automorphic representations of GL(2); in particular, the correspondence between Hecke eigenforms in the classical sense and automorphic representations. • The Jacquet-Langlands correspondence, relating automorphic forms on GL(2) with those on a division algebra. • ...
متن کامل