Related papers: A local-global principle for power maps

In this article we analyze the global diffeomorphism property of polynomial maps $F:\mathbb{R}^n\rightarrow\mathbb{R}^n$ by studying the properties of the Newton polytopes at infinity corresponding to the sum of squares polynomials…

For a local field $F$ we consider tamely ramified principal series representations $V$ of $G={\rm GL}_{d+1}(F)$ with coefficients in a finite extension $K$ of ${\mathbb Q}_p$. Let $I_0$ be a pro-$p$-Iwahori subgroup in $G$, let ${\mathcal…

Let K be a function field and let (f) be a principal prime ideal of the ring A, which is a subring of K. Let phi: A --> K {tau} be a Drinfeld module. In this paper we consider the problem whether a point P in K which is a phi(f)-fold…

Let ${\mathcal G}$ be an infinite family of connected graphs and let $k$ be a positive integer. We say that $k$ is ${\it forcing}$ for ${\mathcal G}$ if for all $G \in {\mathcal G}$ but finitely many, the following holds. Any…

We compute the rank of the fundamental group of an arbitrary connected component of the space map(X, Y) for X and Y nilpotent CW complexes with X finite. For the general component corresponding to a homotopy class f : X --> Y, we give a…

Let $L^0$ be the algebra of equivalence classes of real valued random variables on a given probability space, and $(L^0)^n$ the $n$-ary Cartesian power of $L^0$ for each integer $n\geq 2$. We consider $(L^0)^n$ as a free module over $L^0$…

A real polynomial $f$ is called local nonnegative at a point $p$, if it is nonnegative in a neighbourhood of $p$. In this paper, a sufficient condition for determining this property is constructed. Newton's principal part of $f$ (denoted as…

Let ${\mathfrak g}$ be a finite dimensional simple Lie algebra over an algebraically closed field $K$ of characteristic $0$. A linear map $\varphi:{\mathfrak g}\to {\mathfrak g}$ is called a local automorphism if for every $x$ in…

We extend the Local-to-Global-Principle used in the proof of convexity theorems for momentum maps to not necessarily closed maps whose target space carries a convexity structure which need not be based on a metric. Using a new factorization…

We show that the backward orbit conjecture is true for powering map $\phi(z)=z^d$ over a function field $K$ with a finite field of constants, and when $d$ is relatively prime to the characteristic of $K$.

This paper deepens the connections between critically finite rational maps and finite subdivision rules. The main theorem is that if f is a critically finite rational map with no periodic critical points, then for any sufficiently large…

Let $G$ be a finite group and $n_p(G)$ the number of Sylow $p$-subgroups of $G$. In this paper, we prove if $n_p(G)<p^2$ then almost all numbers $n_p(G)$ are a power of a prime.

We give sharp conditions on a local biholomorphism $F:X \to \mathbb C^{n}$ which ensure global injectivity. For $n \geq 2$, such a map is injective if for each complex line $l \subset \mathbb C^{n}$, the pre-image $F^{-1}(l)$ embeds…

We prove the following theorem: Fibered Power Theorem: Let $X\rar B$ be a smooth family of positive dimensional varieties of general type, with $B$ irreducible. Then there exists an integer $n>0$, a positive dimensional variety of general…

We provide sufficient conditions for a mapping $f:R^{n}\rightarrow R^{n}$ to be a global diffeomorphism in case it is strictly (Hadamard) differentiable. We use classical local invertibility conditions together with the non-smooth critical…

Let $d$ be a positive integer and $\mathbb H$ be an integrally closed subring of a global function field $F$. The purpose of this paper is to provide a general sieve method to compute densities of subsets of $\mathbb H^d$ defined by local…

We discuss local-global principles for the existence of Levi factors (i.e., complements to the unipotent radical) for linear algebraic groups over one-variable function fields. We give examples of disconnected groups that fail the…

Let $K$ be a number field, let $\phi \in K(t)$ be a rational map of degree at least 2, and let $\alpha, \beta \in K$. We show that if $\alpha$ is not in the forward orbit of $\beta$, then there is a positive proportion of primes ${\mathfrak…

Jacobian conjectures (that nonsingular implies a global inverse) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The birational…

Let K be a number field or a function field, let F:P^1 --> P^1 be a rational map of degree at least two defined over K, let P be a point in P^1(K) having infinite F-orbit, and let Z be a finite subset of Z. We prove a local-global criterion…