Related papers: Level-raising for automorphic forms on $GL_n$

In this article, we improve our main results from \emph{Chow groups and $L$-derivatives of automorphic motives for unitary groups} in two direction: First, we allow ramified places in the CM extension $E/F$ at which we consider…

In this work we provide a level raising theorem for $\mod \lambda^n$ modular Galois representations. It allows one to see such a Galois representation that is modular of level $N$, weight 2 and trivial Nebentypus as one that is modular of…

Let n be either 2, or an odd integer greater than 1, and fix a prime p > 2(n + 1). Under standard "adequate image" assumptions, we show that the set of components of n-dimensional p-adic potentially semistable local Galois deformation rings…

We prove that if $f:X \rightarrow A$ is a morphism from a smooth projective variety $X$ to an abelian variety $A$ over a number field $K$, and $G$ is a subgroup of automorphisms of $X$ satisfying certain properties, and if a prime $p$…

Recently, the problem of bounding the sup norms of $L^2$-normalized cuspidal automorphic newforms $\phi$ on $\text{GL}_2$ in the level aspect has received much attention. However at the moment strong upper bounds are only available if the…

In this article we perform an extensive study of the spaces of automorphic forms for GL(2) of weight two and level N, for N an ideal in the ring of integers of the quartic CM field generated by the twelfth roots of unity. This study is…

Let $p$ and $\ell$ be distinct primes, and $\rho$ be an orthogonal or symplectic representation of the absolute Galois group of an $\ell$-adic field over a finite field of characteristic $p$. We define and study a liftable deformation…

In this paper we establish a new case of Langlands functoriality. More precisely, we prove that the tensor product of the compatible system of Galois representations attached to a level-1 classical modular form and the compatible system…

Let $p$ be a prime number, $n>2$ an integer, and $F$ a CM field in which $p$ splits completely. Assume that a continuous automorphic Galois representation…

Given a polynomial $f$ with coefficients in a field of prime characteristic $p$, it is known that there exists a differential operator that raises $1/f$ to its $p$th power. We first discuss a relation between the `level' of this…

Given a smooth hyperplane section $H$ of a rational homogeneous space $G/P$ with Picard number one, we address the question whether it is always possible to lift an automorphism of $H$ to the Lie group $G$, or more precisely to Aut$(G/P)$.…

Let $E$ be an algebraic extension of a global field $E_{0}$ with a nontrivial Brauer group Br$(E)$, and let $P(E)$ be the set of those prime numbers $p$, for which $E$ does not equal its maximal $p$-extension $E(p)$. This paper shows that…

Behind this sophisticated title hides an elementary exercise on Clifford theory for index two subgroups and self-dual/conjugate-dual representations. When applied to semi-simple representations of the Weil-Deligne group $W'_F$ of a non…

We prove that $\bar {\mathbb Q}_\ell$-local systems of bounded rank and ramification on a smooth variety $X$ defined over an algebraically closed field $k$ of characteristic $p\neq \ell$ are tamified outside of codimension $2$ by a finite…

We prove an unconditional power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL_2 over any number field which is not totally real. Our proof involves the theory of p-adically…

Let L be a countable elementary language, N be a Fraisse limit. We consider free amalgamation for L-structures where L is arbitrary. If free amalgamation for finitely generated substructures exits in N, then it is a stationary independece…

We prove an integrality result for the value at s=1 of the adjoint L-function associated to a cohomological cuspidal automorphic representation on GL(n) over any number field. We then show that primes (outside an exceptional set) dividing…

We classify polynomial models for real hypersurfaces in $\mathbb C^N$, which admit nonlinearizable infinitesimal CR automorphisms. As a consequence, this provides an optimal 1-jet determination result in the general case. Further we prove…

Let $f$ be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric power lifting $\mathrm{Sym}^n f$ for every $n \geq 1$. We establish the same result for a more general class of cuspidal Hecke eigenforms, including…

Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let l be a prime number different from p. We develop a theory of l-modular types for the group…