Related papers: Global uniqueness of small representations

We prove local-global compatibility results at $\ell=p$ for the torsion automorphic Galois representations constructed by Scholze, generalising the work of Caraiani--Newton. In particular, we verify, up to a nilpotent ideal, the…

In this paper, a strong multiplicity one theorem for Katz modular forms is studied. We show that a cuspidal Katz eigenform which admits an irreducible Galois representation is in the level and weight old space of a uniquely associated Katz…

We show that if the automorphism group of a projective variety is torsion, then it is finite. Motivated by Lang's conjecture on rational points of hyperbolic varieties, we use this to prove that a projective variety with only finitely many…

It is known that every finite group can be represented as the full group of automorphisms of a suitable compact dessin d'enfant. In this paper, we give a constructive and easy proof that the same holds for any countable group by considering…

Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions…

Let $G$ be a locally compact totally disconnected topological group. Under a necessary mild assumption, we show that the irreducible unitary representations of $G$ are uniformly admissible if and only if the irreducible smooth…

We prove a version of Gabriel's theorem for locally finite-dimensional representations of infinite quivers. Specifically, we show that if $\Omega$ is any connected quiver, the category of locally finite-dimensional representations of…

The number of singularities, counted with multiplicity, of a generic codimension one holomorphic distribution on a compact toric orbifold is determined. As a consequence, we give the classification of regular distributions on rational…

We show that Alexander's extendibility theorem for a local automorphism of the unit ball is valid also for a local automorphism $f$ of a pseudoellipsoid $\E^n_{(p_1, ..., p_{k})} \= \{z \in \C^n : \sum_{j= 1}^{n - k}|z_j|^2 + |z_{n-k+1}|^{2…

We generalize Wagoner's representation of the automorphism group of a two-sided subshifts of finite type as the fundamental group of a certain CW-complex to groupoids having a certain refinement structure. This significantly streamlines the…

We prove the automorphism conjecture for ordered sets of width less than or equal to 11. The proof supports the meta conjecture that a large number of automorphisms is achievable only as some type of product of independent automorphisms on…

Cartan's uniqueness theorem does not hold in general for CR mappings, but it does hold under certain conditions guaranteeing extendibility of CR functions to a fixed neighborhood. These conditions can be defined naturally for a wide class…

We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.

Recent results by Abert, Bergeron, Biringer et al., Finis, Lapid and Mueller, and Shin and Templier have extended the limit multiplicity property to quite general classes of groups and sequences of level subgroups. Automorphic…

Let X be a flexible variety of F be an isomorphism of closed one-dimensional subschemes of $X$. We develop criteria which guarantee that F extends to au automorphism of X.

We give a short, mostly elementary and self-contained proof of the classical result that the groups of diffeomorphisms, homeomorphisms, and homotopy equivalences of a surface have the same group of connected components.

We show that if a field k contains sufficiently many elements(for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A\otimes_kK), where A is a…

Let $F$ be the function field of a projective smooth geometrically connected curve $X$ defined over a finite field $\mathbb{F}_q$. Let $G$ be a split semisimple algebraic group over $\mathbb{F}_q$. Let $S$ be a non-empty finite set of…

For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open)…

We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…