相关论文: A counterexample to a conjecture of S.E. Morris

We prove that for every compact, connected, differentiable 3--manifold $M$ there is a compact complex manifold $X$ which can be obtained from projective 3--space by a sequence of smooth, real blow ups and downs such that $M$ is…

We prove that a submaximal plane curve (i.e., an irreducible counterexample to Nagata's conjecture) with r singular points has sequence of multiplicities (m, n, ..., n) with m<sn for every integer with ((s-1)(s+2))^2 > 6.76(r-1).

In this paper we first show that for a locally compact amenable group $G$, every proper abstract Segal algebra of the Fourier algebra on $G$ is not approximately amenable; consequently, every proper Segal algebra on a locally compact…

We prove the following result, which is motivated by the recent work of Kurano and Roberts on Serre's positivity conjecture. Assume that (R,m) is a local ring with finitely-generated module M such that R/ann(M) is quasi-unmixed and contains…

In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to study several optimization setups including closed CMC…

It is proved that a discrete group $G$ is amenable if and only if for every unitary representation of $G$ in an infinite-dimensional Hilbert space $\cal H$ the maximal uniform compactification of the unit sphere $\s_{\cal H}$ has a…

Let $L^1_\om(G)$ be a Beurling algebra on a locally compact abelian group $G$. We look for general conditions on the weight which allows the vanishing of continuous derivations of $L^1_\om(G)$. This leads us to introducing vector-valued…

The aim of this note is to obtain results about when the norm of a projective tensor product is strongly subdifferentiable. We prove that if $X\hat{\otimes}_\pi Y$ is strongly subdifferentiable and either $X$ or $Y$ has the metric…

In this paper we prove that a pure, regular, totally odd, polarizable weakly compatible system of $l$-adic representations is potentially automorphic. The innovation is that we make no irreducibility assumption, but we make a purity…

We introduce the notions of $\varepsilon$-approximate fixed point and weak $\varepsilon$-approximate fixed point. We show that for a group of unitary matrices even the existence of a nontrivial weak $\varepsilon$-approximate fixed point for…

Let $K$ be a number field, let $X$ be a smooth integral variety over $K$, and assume that there exists a finite set of finite places $S$ of $K$ such that the $S$-integral points on $X$ are dense. Then the combined conjectures of Campana and…

Consider the semialgebraic structure over the real field. More generally, let an ominimal structure be over a real closed field. We show that a definable metric space X with a definable metric d is embedded into a Euclidean space so that…

We provide a counterexample to a conjecture of Hildebrand which states that if $\S$ has positive lower density and is stable i.e. for all $d$, $n$ is in $\mathcal{S}$ if and only if $dn$ is in $\mathcal{S}$ except on a set of density $0$…

In this paper we consider a notion of nonmeasurablity with respect to Marczewski and Marczewski-like tree ideals $s_0$, $m_0$, $l_0$, and $cl_0$. We show that there exists a subset $A$ of the Baire space $\omega^\omega$ which is $s$-, $l$-,…

We show that, if a simple $C^{*}$-algebra $A$ is topologically finite-dimensional in a suitable sense, then not only $K_{0}(A)$ has certain good properties, but $A$ is even accessible to Elliott's classification program. More precisely, we…

We prove a result about extension of a minimal AF-equivalence relation R on the Cantor set X, the extension being `small' in the sense that we modify R on a thin closed subset Y of X. We show that the resulting extended equivalence relation…

For a finite and positive measure space $(\Omega,\Sigma,\mu)$ and any weakly compact convex subset of $L\sp\infty(\Omega,\Sigma,mu)$, a fixed point theorem for a class of nonexpansive self-mappings is proved. An analogous result is obtained…

The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey theoretic reformulation of amenability constitutes a considerable weakening of the Folner…

Let $\rho_\ell$ be a semisimple $\ell$-adic representation of a number field $K$ that is unramified almost everywhere. We introduce a new notion called weak abelian direct summands of $\rho_\ell$ and completely characterize them, for…

A well-known theorem of Day and Dixmier states that any uniformly bounded representation of an amenable locally compact group $G$ on a Hilbert space is similar to a unitary representation. Within the category of locally compact quantum…