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
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...
-adic -functions for unitary Shimura varieties. I: Construction of the Eisenstein measure.
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