Related papers: On $p$-schemes of order $p^3$

For any algebra $A$ over an algebraically closed field $\mathbb{F}$, we say that an $A$-module $M$ is Schurian if $\mathrm{End}_A(M) \cong \mathbb{F}$. We say that $A$ is Schurian-finite if there are only finitely many isomorphism classes…

We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schr\"odinger equations driven by additive It\^o noise. The class of nonlinearities of interest includes nonlocal…

Let $G$ be a finite $p$-group and $N$ be a normal subgroup of $G$, with $|N|=p^n$ and $|G/N|=p^m$. A result of Ellis (1998) shows that the order of the Schur multiplier of such a pair $(G,N)$ of finite $p$-groups is bounded by $…

A theorem of Green says that a line bundle of degree at least $2g+1+p$ on a smooth curve $X$ of genus $g$ has property $N_p$. We prove a similar conclusion for certain singular, reducible curves $X$ under suitable degree bounds over all…

In this article we prove a reducibility result for the linear Schr\"odinger equation on a Zoll manifold with quasi-periodic in time pseudo-differential perturbation of order less or equal than $1/2$. As far as we know, this is the first…

We prove that for any prime number $p\ge 3$, there exists a positive number $\kappa_p$ such that $\chi(\mathcal{O}_X)\ge \kappa_pc_1^2$ holds true for all algebraic surfaces $X$ of general type in characteristic $p$. In particular,…

For each $\Pi^0_1$ $S\subseteq \mathbb{N}$, let the $S$-square shift be the two-dimensional subshift on the alphabet $\{0,1\}$ whose elements consist of squares of 1s of various sizes on a background of 0s, where the side length of each…

Any non-abelian finite $p$-group has a non-inner automorphism of order $p$.

We present the example of l^p spaces, where we examine results of topological and algebraic genericity and spaceability. At the end of the paper we include a project with other chains of spaces, mainly of holomorphic functions, as Hardy…

We derive a formula which is a lower bound on the dimension of trivariate splines on a tetrahedral partition which are continuously differentiable of order $r$ in large enough degree. While this formula may fail to be a lower bound on the…

Let U be a basepoint free four-dimensional subpace of the space of sections of bidegree (a,b) on X = P^1 x P^1, with a and b at least 2. The sections corresponding to U determine a regular map from X to P^3. We show that there can be at…

In this paper we verify the Strauss conjecture for semilinear wave equations on asymptotically Euclidean manifolds when n=3,4, we also give an almost sharp life span for the subcritical case $2\le p<p_c$ when n=3. The main ingredients…

In this paper we study properties of the triangular projection ${\mathcal P}_n$ on the space of $n\times n$ matrices. The projection ${\mathcal P}_n$ annihilates the entries of an $n\times n$ matrix below the main diagonal and leaves the…

Let $X$ be a topological space. A subset of $C(X)$, the space of continuous real-valued functions on $X$, is a partially ordered set in the pointwise order. Suppose that $X$ and $Y$ are topological spaces, and $A(X)$ and $A(Y)$ are subsets…

We introduce a method to determine if n-dimensional smooth subvarieties of an ambient space of dimension at most 2n &#8722; 2 inherit the Picard group from the ambient space (as it happens when the ambient space is a projective space,…

We study the Schlesinger system of partial differential equations in the case when the unknown matrices of arbitrary size $(p\times p)$ are triangular and the eigenvalues of each matrix form an arithmetic progression with a rational…

Part of these notes was written as the author's 2013 master thesis. For proper flat schemes over a complete discrete valuation ring of mixed characteristic, we construct an isomorphism of certain subgroups of the Picard group and the first…

We prove that every quasisymmetric self-homeomorphism of the standard 1/3-Sierpi\'nski carpet $S_3$ is a Euclidean isometry. For carpets in a more general family, the standard $1/p$-Sierpi\'nski carpets $S_p$, $p\ge 3$ odd, we show that the…

In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schr\"odinger equations to higher-order Schr\"odinger equations with a more general nonlinearity. More precisely, we consider a…

In this paper, we consider a class of continuous maps characterized by a singularity of order $x^{q/p}$ (with $p,q \in \mathbb{N}$, $p>q$, and $(p,q)=1$) on one side of the discontinuity boundary $\Sigma$ and a linear behaviour on the other…