Automorphic forms, hyperfunction cohomology, and period functions.
Automorphic Forms of Singular Weight are Singular Forms.
Automorphic Forms on Covering Groups of GL(2).
Automorphic forms on Os + 2,2(R) and infinte products.
Automorphic forms on .
Automorphic -functions in the weight aspect.
Automorphic realization of residual Galois representations
We show that it is possible in rather general situations to obtain a finite-dimensional modular representation of the Galois group of a number field as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over , provided one works “potentially.” The proof is based on a close study of the monodromy of the Dwork family of Calabi–Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification...
Automorphic representations and Lefschetz numbers
Automorphic vector bundles on connected Shimura varieties.
Automorphism groups of the modular curves
Automorphismes de courbes modulaires
Automorphy for some l-adic lifts of automorphic mod l Galois representations. II
We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara’s lemma.
Automorphy for some l-adic lifts of automorphic mod l Galois representations
We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), minimally ramified, l-adic lifts of certain automorphic mod l Galois representations of any dimension. We also make a conjecture about the structure of mod l automorphic forms on definite unitary groups, which would generalise a lemma of Ihara for GL2. Following Wiles’ method we show that this...
Average Frobenius distributions for elliptic curves with nontrivial rational torsion
Average values of L-series in function fields.
Averages of twisted elliptic L-functions
-représentations dans le cas relatif
Dans ce travail nous développons un analogue relatif de la théorie de Sen pour les -représentations. On donne des applications à la théorie des représentations -adiques, en la reliant à la théorie des -modules relatifs, et à celle des modules de Higgs -adiques développée par G. Faltings.
Banach-Hecke algebras and -adic Galois representations.
Barnes' identities and representations of GL (2). II. Nonarchimedian local field case.
Base change for Bernstein centers of depth zero principal series blocks
Let be an unramified group over a -adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with -level structure initiated by M. Rapoport and the author in [15].