Related papers: $F_p$-espaces vectoriels de formes diff\'erentiell…

Let $F$ be a field of characteristic $p$ and let $\Omega^n(F)$ be the $F$-vector space of $n$-differential forms. In this work, we will study the annihilator of differential forms, give specific descriptions for special cases and show a…

In this paper we give full classification of rank 3 line arrangements in $\mathbb P^2$ (over a field of characteristic 0) that have a minimal logarithmic derivation of degree 3. The classification presents their defining polynomials, up to…

In this article, we study the properties of a class of functional spaces which arise from the investigation of nonlinear differential equations. We establish some integral inequalities then by applying these inequalities, we prove some…

We address a linearity problem for differentiable vectors in representations of infinite-dimensional Lie groups on locally convex spaces, which is similar to the linearity problem for the directional derivatives of functions.

Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…

Affine structures on a Lie groupoid, including affine $k$-vector fields, $k$-forms and $(p,q)$-tensors are studied. We show that the space of affine structures is a 2-vector space over the space of multiplicative structures. Moreover, the…

Building on work of Gerstenhaber, we show that the space of integrable derivations on an Artin algebra $A$ forms a Lie algebra, and a restricted Lie algebra if $A$ contains a field of characteristic $p$. We deduce that the space of…

Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the…

Graph-based analysis holds both theoretical and applied significance, attracting considerable attention from researchers and yielding abundant results in recent years. However, research on fractional problems remains limited, with most of…

Let F : V --> V be a self-morphism of a quasiprojective variety defined over a number field K and let P be a point in V(K) with infinite orbit under iteration of F. For each prime ideal p of good reduction, let m_p(F,P) be the size of the…

In the first part of the paper the authors study the minimal and maximal extension of a class of weighted pseudodifferential operators in the Fr\'echet space $L^p_{\rm loc}(\Omega)$. In the second one non homogeneous microlocal properties…

In this note, we determine which automorphism subgroups of $\mathrm{Aut}_{\mathbb{F}_q}(\mathbb{F}_q((x)))$ are corresponding to $\mathbb{Z}_p$-extensions or $\mathbb{Z}_p\times\mathbb{Z}_p$-extensions of characteristic $0$ fields.

The purpose of this survey is to explain some recent results about analogies between characteristic 0 and characteristic $p>0$ geometry, and to discuss an infinitesimal variant of motivic cohomology. More specifically, we review results…

In this article we investigate the action of (ramified and unramified) Hecke operators on automorphic forms for the function field of the projective line defined over a finite field and for the group GL_2. We first compute the dimension of…

In this note, it is shown that the differential polynomial of the form $Q(f)^{(k)}-p$ has infinitely many zeros, and particularly $Q(f)^{(k)}$ has infinitely many fixed points for any positive integer $k$, where $f$ is a transcendental…

Let k be a perfect field and let K/k be a finite extension of fields. An arithmetic noncommutative projective line is a noncommutative space equal to the projectivization of the noncommutative symmetric algebra of a k-central two -sided…

This work concerns the problem of relating characteristic numbers of one-dimensional holomorphic foliations of P^n to those of algebraic varieties invariant by them. More precisely: if M is a connected complex manifold, a one-dimensional…

Using the formalism of bar complexes and their relative versions, we give a new, purely algebraic, construction of the so-called universal elliptic KZB connection in arbitrary level. We compute explicit analytic formulae, and we compare our…

We prove that $\mathbb{F}_p$ sketch, a well-celebrated streaming algorithm for frequency moments estimation, is differentially private as is when $p\in(0, 1]$. $\mathbb{F}_p$ sketch uses only polylogarithmic space, exponentially better than…

We prove the existence and uniqueness of a projectively equivariant symbol map (in the sense of Lecomte and Ovsienko) for the spaces $D_p$ of differential operators transforming p-forms into functions. These results hold over a smooth…