Related papers: Griffiths-Schmid conditions for automorphic forms …

We find the number $s_k(p,\Omega)$ of cuspidal automorphic representations of $\mathrm{GSp}(4,\mathbb{A}_{\mathbb{Q}})$ with trivial central character such that the archimedean component is a holomorphic discrete series representation of…

We establish Bernstein-centre type of results for the category of mod $p$ representations of $\mathrm{GL}_2(\mathbb{Q}_p)$. We treat all the remaining open cases, which occur when $p$ is $2$ or $3$. Our arguments carry over for all primes…

We develop a new strategy for studying low weight specializations of $p$-adic families of ordinary modular forms. In the elliptic case, we give a new proof of a result of Ghate--Vatsal which states that a Hida family contains infinitely…

The aim of this paper is to prove the weight-monodromy conjecture (Deligne's conjecture on the purity of monodromy filtration) for varieties p-adically uniformized by the Drinfeld upper half spaces of any dimension. The ingredients of the…

In this paper we show that Atkin and Swinnerton-Dyer type of congruences hold for weakly modular forms (modular forms that are permitted to have poles at cusps). Unlike the case of original congruences for cusp forms, these congruences are…

In this article, we prove results about the cohomology of compact unitary group Shimura varieties at split places. In nonendoscopic cases, we are able to give a full description of the cohomology, after restricting to integral Hecke…

We prove formulae for the Hodge numbers of big resolutions of singular hypersurfaces satisfying a Bott-type vanishing condition.

We prove that the Galois pseudo-representation valued in the mod $p^n$ cuspidal Hecke algebra for GL(2) over a totally real number field $F$, of parallel weight $1$ and level prime to $p$, is unramified at any place above $p$. The same is…

We show that the systems of Hecke eigenvalues occurring in the spaces of Siegel modular forms (mod p) of fixed dimension g, fixed level N, and varying weight, are the same as the systems occurring in the spaces of Siegel cusp forms with the…

We prove a variant of the Theorem of Ito-Michler, investigating the properties of finite groups where a prime number $p$ does not divide the degree of any irreducible character left invariant by some Galois automorphism $\sigma$ of order…

We prove that, for fixed tame level (N,p) = 1, there are only finitely many Hecke eigenforms f of level Gamma_1(N) and even weight with a_p(f) = 0 which are not CM.

Zagier introduced toroidal automorphic forms to study the zeros of zeta functions: an automorphic form on GL_2 is toroidal if all its right translates integrate to zero over all nonsplit tori in GL_2, and an Eisenstein series is toroidal if…

We prove that for any Hecke eigenform f of level 1 and arbitrary weight there is a self-dual cuspidal automorphic form $\pi$ of $GL_6(\Q)$ corresponding to $\Symm^5 (f)$, i.e., such that the system of Galois representations attached to…

We show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some…

Let P be a free Poisson algebra in two variables over a field of characteristic zero. We prove that the automorphisms of P are tame and that the locally nilpotent derivations of P are triangulable.

We study statistical properties of Fourier coefficients of automorphic forms on GL(n). For most Hecke-Maass cusp forms, we give the asymptotic number of nonvanishing coefficients, show that there is a positive proportion of sign changes…

We show that the Taylor-Wiles method can be applied to the cohomology of a Shimura variety $S$ of PEL type attached to a unitary similitude group $G$, with coefficients in the coherent sheaf attached to an automorphic vector bundle $\CF$ ,…

We prove that the Jacquet-Langlands correspondence for cohomological automorphic forms on quaternionic Shimura varieties is realized by a Hodge class. Conditional on Kottwitz's conjecture for Shimura varieties attached to unitary similitude…

We prove a rigidity theorem for the Poisson automorphisms of the function fields of tori with quadratic Poisson structures over fields of characteristic 0. It gives an effective method for classifying the full Poisson automorphism groups of…

While vector-valued automorphic forms can be defined for an arbitrary Fuchsian group $\Gamma$ and an arbitrary representation $R$ of $\Gamma$ in GL$(n,{\mathbb C})$, their existence has been established in the literature only when…