Related papers: Local-global principles in circle packings

We study a local to global principle for certain higher zero-cycles over global fields. We thereby verify a conjecture of Colliot-Th\'el\`ene for these cycles. Our main tool are the Kato conjectures proved by Jannsen, Kerz and Saito. Our…

The ascent and descent of the Mittag-Leffler property were instrumental in proving Zariski locality of the notion of an (infinite dimensional) vector bundle by Raynaud and Gruson in \cite{RG}. More recently, relative Mittag-Leffler modules…

Let $K$ be the function field of a smooth projective geometrically integral curve over a finite extension of $\mathbb{Q}_p$. Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local-global and weak…

We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a…

We show that there exist infinitely many commensurability classes of finite volume hyperbolic 3-manifolds whose fundamental group contains a subgroup which is locally free but not free. The main technical tool is the fact that a collection…

This paper aims at developing a "local--global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the…

This paper studies "pro-excision" for the K-theory of one-dimensional (usually semi-local) rings and its various applications. In particular, we prove Geller's conjecture for equal characteristic rings over a perfect field of finite…

We compute the universal deformations of cuspidal representations $\pi$ of $\GL_2(F)$ over an algebraically closed field of characteristic $l$, where $F$ is a local field of residue characteristic $p$ not equal to $l$. When $\pi$ is…

We construct a quadratic curvature theory of gravity whose graviton propagator around the Minkowski background respects wordline inversion symmetry, the particle approximation to modular invariance in string theory. This symmetry…

In this paper, we assume that $G$ is a finitely generated torsion free non-elementary Kleinian group with $\Omega(G)$ nonempty. We show that the maximal number of elements of $G$ that can be pinched is precisely the maximal number of rank 1…

The concept of Faltings' local-global principle for the in dimension $< n$ of local cohomology modules over a Noetherian ring $R$ is introduced, and it is shown that this principle holds at levels 1, 2. We also establish the same principle…

Let $K/F$ be a finite Galois extension of number fields. It is well known that the Tchebotarev density theorem implies that an irreducible, finitely ramified $p$-adic representation $\rho$ of the absolute Galois group of $K$ is determined…

We consider large random matrices $X$ with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical…

In this paper, which is the natural continuation and generalization of Fesenko's non-abelian reciprocity map, we extend the theory of Fesenko to infinite $APF$-Galois extensions $L$ over a local field $K$, with finite residue-class field…

The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…

We propose an operator generalization of the Li-Haldane conjecture regarding the entanglement Hamiltonian of a disk in a 2+1D chiral gapped groundstate. The logic applies to regions with sharp corners, from which we derive several universal…

An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N-3) functionally independent constants of the motion. Among them, two…

In the first part of this article we discuss the relative cases of Quillen-Suslin's local-global principle for the general quadratic (Bak's unitary) groups, and its applications for the (relative) stable and unstable $\mathrm{K}_1$-groups.…

We obtain a solution to a bordism version of Gromov's linearity problem over a large family of acyclic groups, for manifolds with arbitrary dimension. Every group embeds into some acyclic group in this family. Thus, the linear bordism…

We prove matching direct and inverse theorems for uniform polynomial approximation with $A^*$ weights (a subclass of doubling weights suitable for approximation in the $L_\infty$ norm) having finitely many zeros and not too "rapidly…