Maass Operators and Eisenstein Series.
Non-vanishing of L-functions of 2 x 2 unitary groups.
L-functions and periods of polarized regular motives.
Kubert-lang units and elliptic curves without complex multiplication
-adic representations arising from descent on abelian varieties
Period invariants of Hilbert modular forms, II
Arithmetic vector bundles and automorphic forms on Shimura varieties, II
Systematic Growth of Mordell-Weil Groups of Abelian Varieties in Towers of Number Fields.
The Rationality of Holomorphic Eisenstein Series.
Special values of zeta functions attached to Siegel modular forms
-adic -functions for unitary Shimura varieties. I: Construction of the Eisenstein measure.
Boundary cohomology of Shimura varieties. II. Hodge theory at the boundary.
Boundary cohomology of Shimura varieties. I. Coherent cohomology on toroidal compactifications
A note on trilinear forms for reducible representations and Beilinson's conjectures
We extend Prasad’s results on the existence of trilinear forms on representations of of a local field, by permitting one or more of the representations to be reducible principal series, with infinite-dimensional irreducible quotient. We apply this in a global setting to compute (unconditionally) the dimensions of the subspaces of motivic cohomology of the product of two modular curves constructed by Beilinson.
Singular Holomorphic Representations and Singular Modular Forms.
l-adic representations associated to modular forms over imaginary quadratic fields.
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...
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...
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