Related papers: On congruent isomorphisms for tori

A (non-commutative) Ulam quasimorphism is a map $q$ from a group $\Gamma$ to a topological group $G$ such that $q(xy)q(y)^{-1}q(x)^{-1}$ belongs to a fixed compact subset of $G$. Generalizing the construction of Barge and Ghys, we build a…

We construct cohomology theories for $(\varphi, \tau)$-modules, and study their relation with cohomology of $(\varphi, \Gamma)$-modules, as well as Galois cohomology. Our method is axiomatic, and can treat the \'etale case, the…

The aim of this paper is to study a problem raised by N. C. Phillips concerning the existence of Takai duality for $L^p$ operator crossed products $F^{p}(G,A,\alpha)$, where $G$ is a locally compact Abelian group, $A$ is an $L^{p}$ operator…

In this paper, we show that for reduced homotopy endofunctors of spaces, F, and for all $n \geq 1$ there are adjoint functors $R_n, L_n$ with $T_n F \simeq R_n F L_n$, where $P_n F$ is the $n$-excisive approximation to $F$, constructed by…

In this paper, we extend the Goldman-Millson Theorem for $L_\infty$ algebras. We consider two $L_\infty$ algebras $L$ and $\tilde{L}$ endowed with descending, bounded above and complete filtrations compatible with the $L_\infty$ structures…

We show that various actions of topological conformal theories that were suggested recentely are particular cases of a general action. We prove the invariance of these models under transformations generated by nilpotent fermionic generators…

Study of the matrix-level affine algebra $U_{m,K}$ is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of $U_{m,K}$ modular-invariant partition functions. Here we connect the…

Given a small category C, a C-module M is a functor from C to the category of finite-dimensional vector spaces over a field k. Associated to M is its local structure, given as a functor from C to the category of bi-closed multi-flags over…

Given a pair of number fields with isomorphic rings of adeles, we construct bijections between objects associated to the pair. For instance we construct an isomorphism of Brauer groups that commutes with restriction. We additionally…

Let G be a Lie group equipped with a left-invariant semi-Riemannian metric. Let K be a semisimple subgroup of G generating a left-invariant conformal foliation F of codimension two on G. We then show that the foliation F is minimal. This…

This article investigates congruences of $\mathfrak{p}$-adic representations arising from effective $A$-motives defined over a global function field $K$. We give a criterion for two congruent $\mathfrak{p}$-adic representations coming from…

The present work is devoted to compact completely solvable solvmanifolds which admit Kahlerian metrics whose Kahler forms are homogeneous. In particular, we show that such manifolds are diffeomorphic to flat tori. Our proof is based on…

Let $G_1$ and $G_2$ be Lie groups furnished with bi-invariant metrics and $f:G_1\rightarrow G_2$ be a Lie group homomorphism which is also a minimal isometric immersion. If $G_1$ is compact and connected, we prove that either $G_1$ is…

Let $R$ be a commutative noetherian ring and $f: X \to \mathrm{Spec} R$ a proper smooth morphism, of relative dimension $n$. From Hartshorne, Residues and Duality, Springer, 1966, one knows that the trace map $\mathrm{Tr}_f :…

Suppose $G$ is an amenable locally compact group. If $\{F_\gamma\} = \{F_\gamma\}_{\gamma\in\Gamma}$ is a F\o{}lner net for $G$, associate it with the net $\{\chi_{F_\gamma} / |F_\gamma|\} \subset L_1(G) \subset L_\infty^*(G)$. Thus, every…

We address a variant of Zariski Cancellation Problem, asking whether two varieties which become isomorphic after taking their product with an algebraic torus are isomorphic themselves. Such cancellation property is easily checked for…

This work results from a study of Nicholas Kuhn's paper entitled "Generic representation theory of finite fields in nondescribing characteristic". Our goal is to abstract the categorical structure required to obtain an equivalence between…

In general, Lagrangian Floer homology - if well-defined - is not isomorphic to singular homology. For arbitrary closed Lagrangian submanifolds a local version of Floer homology is defined in [Flo89, Oh96] which is isomorphic to singular…

This paper is devoted to the study of minimal immersions of flat $n$-tori into spheres, especially those immersed by the first eigenfunctions (such immersion is called $\lambda_1$-minimal immersion), which also play important roles in…

We try to build, provably in ZFC, for a first order T a model in which any isomorphism between two Boolean algebras is definable. The problem, compared to [Sh:384], is with pseudo-finite Boolean algebras. A side benefit is that we do not…