Related papers: On endoscopic p-adic automorphic forms for SL(2)

We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…

We prove that every $2$-local automorphism on a finite-dimensional semi-simple Lie algebra $\mathcal{L}$ over an algebraically closed field of characteristic zero is an automorphism. We also show that each finite-dimensional nilpotent Lie…

The loop space $L\mathbb{P}^n$ of the complex projective space $\mathbb{P}^n$ consisting of all $C^k$ or Sobolev $W^{k, \, p}$ maps $S^1 \to \mathbb{P}^n$ is an infinite dimensional complex manifold. We identify a class of holomorphic…

In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. In the first part, we use Hodge theory and deformation theory to study the deformations of automorphisms of complex…

The notion of Lie $H$-pseudoalgebra is a higher-dimensional analogue of Lie conformal algebras. In this paper, we classify the equivalence classes of non-abelian extensions of a Lie $H$-pseudoalgebra $L$ by another Lie $H$-pseudoalgebra $M$…

This is an attempt at a practical and essentially self-contained theory of automorphic representations in the framework $$\hbox{$L^2(\varGamma\backslash\r{G})$ with $\r{G}=\r{PSL}(2,\B{R})$ and $\varGamma=\r{PSL}(2,\B{Z})$.}$$

I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level $G(Z-hat)$ and various small weights for an example of a rank 3 unitary…

In this paper, we use variational methods to prove the existence of heteroclinic solutions for a class of non-autonomous second-order equation.

We give a construction of $p$-adic Asai $L$-functions for cohomological cuspidal automorphic representations of ${\rm GL}_2$ over CM fields. If the base field is imaginary quadratic, Loeffler-Williams recently constructed the $p$-adic Asai…

Given a cuspidal Hilbert modular eigenform $\pi$ of parallel weight 2 and a nonarchimedian place $\mathfrak p$ of the underlying totally real field such that the local component of $\pi$ at $\mathfrak p$ is the Steinberg representation, one…

We attach p-adic L-functions to critical modular forms and study them. We prove that those L-functions fit in a two-variables p-adic L-function defined locally everywhere on the eigencurve.

We explicitly construct a dynamically incoherent partially hyperbolic endomorphisms of $\mathbb{T}^2$ in the homotopy class of any linear expanding map with integer eigenvalues. These examples exhibit branching of centre curves along…

We apply the endoscopic classification of automorphic forms on U(3) to prove a case of a conjecture of Sarnak and Xue on cohomology growth.

In this paper, we decompose the space of nearly holomorphic Hilbert-Siegel automorphic forms as representations of the adele group under certain assumptions. We also give an application for classical holomorphic Hilbert-Siegel modular…

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

We give a lattice-theoretic classification of non-symplectic automorphisms of prime order of irreducible holomorphic symplectic manifolds of OG10 type. We determine which automorphisms are induced by a non-symplectic automorphism of prime…

We give a way to construct group of pseudo-automorphisms of rational varieties of any dimension that fix pointwise the image of a cubic hypersurface of $P^n. These group are free products of involutions, and most of their elements have…

We compute the arithmetic L-invariants (of Greenberg-Benois) of twists of symmetric powers of p-adic Galois representations attached to Iwahori level Hilbert modular forms (under some technical conditions). Our method uses the automorphy of…

There is a well-established procedure of assigning a strong homotopy Lie algebra of local observables to a multisymplectic manifold which can be regarded as part of a categorified Poisson structure. For a 2-plectic manifold, the resulting…

We give a construction of non-ordinary $p$-adic families of classes in the cohomology of locally symmetric spaces associated to spherical pairs of reductive groups. In the \'etale case, we show how to map these classes into Galois…