Related papers: Positive characteristic Poincar\'e Lemma

Theorem. Let M be a compact, connected, oriented smooth Riemannian n-manifold with non-empty boundary. Then the cohomology of the complex (Harm*(M),d) of harmonic forms on M is given by the direct sum H^p(Harm*(M),d) = H^p(M;R) +…

The strength of a homogeneous polynomial (or form) is the smallest length of an additive decomposition expressing it whose summands are reducible forms. Using polynomial functors, we show that the set of forms with bounded strength is not…

It is shown that the $p$-Poincar\'e inequality holds on an open set $\Omega$ in $\mathbb{R}^n$ if and only if the strict $p$-capacitary inradius of $\Omega$ is finite. To that end, new upper and lower bounds for the infimum for the…

We obtain very sharp results about the lack of validity of the Poincare lemma for the tangential Cauchy Riemann equations, acting on tangential forms, tangential to a CR manifold M of general CR dimension n, and general CR codimension k.…

Let X be a noetherian scheme defined over an algebraically closed field of positive characteristic p, and G be a finite group, of order divisible by p, acting on X. We introduce a refinement of the equivariant K-theory of X to take into…

If $V$ is a smooth projective variety defined over a local field $K$ with finite residue field, so that its \'etale cohomology over the algebraic closure $\bar{K}$ is supported in codimension 1, then the mod $p$ reduction of a projective…

We construct $N$-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ which generalize the usual complex $(N=2)$ of differential forms. Although, for $N\geq 3$, the generalized cohomology of these…

The radial index of a 1-form on a singular set is a generalization of the classical Poincar\'e-Hopf index. We consider different classes of closed semi-analytic sets in R^n that contain 0 in their singular locus and we relate the radial…

The general term of the Poincare normalizing series is explicitly constructed for non-resonant systems of ODE's in a large class of equations. In the resonant case, a non-local transformation is found, which exactly linearizes the ODE's and…

The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose $K$ is a compact set in the complex plane and 0 belongs to the boundary $\partial K$. Let ${\cal A}(K)$ denote the space of all functions $f$ on $K$…

The p-cohomology of an algebraic variety in characteristic p lies naturally in the category $D_{c}^{b}(R)$ of coherent complexes of graded modules over the Raynaud ring (Ekedahl-Illusie-Raynaud). We study homological algebra in this…

This paper is devoted, first of all, to give a complete unified proof of the Characterization Theorem for compact generalized $p-$K\"ahler manifolds (Theorem 3.2). The proof is based on the classical duality between "closed" positive forms…

Starting from the problem of describing cohomological invariants of Poisson manifolds we prove in a sense a ``no-go'' result: the differential graded Lie algebra of de Rham forms on a smooth Poisson manifold is formal.

Let K be a complete discretely valued field with residue field k of characteristic p>0. There is a duality theory for cohomology with coefficients in commutative finite K-group schemes in the following cases : char(K)=0 and k finite (Tate),…

Let $p$ be a nonconstant form in $\mathbb{R}[x_1,\dots,x_n]$ with $p(1,\dots,1)>0$. If $p^m$ has strictly positive coefficients for some integer $m\ge1$, we show that $p^m$ has strictly positive coefficients for all sufficiently large $m$.…

The more important difference between Riemann and pseudo-Riemann manifolds is the metric signature and its theoretical consequences. The practical application for Physics Theories becomes often impossible due to the signature consequences.…

Let $p$ be a prime. In this paper we give a proof of the followingresult: A valued field $(K,v)$ of characteristic $p \textgreater{} 0$ is$p$-henselian if and only if every element of strictly positivevaluation if of the form $x^p - x$ for…

The linear homotopy theory for codifferential operator on Riemannian manifolds is developed in analogy to a similar idea for exterior derivative. The main object is the cohomotopy operator, which singles out a module of anticoexact forms…

Let $p$ be a prime, let $K$ be a finite extension of $\mathbb{Q}_p$, and let $n$ be a positive integer. We construct equivalences of categories between continuous $p$-adic representations of the $n$-fold product of the absolute Galois group…

The purpose of this paper is to explain how the identities of various fundamental lemmas fall within the scope of the transfer principle, a general result that allows to transfer theorems about identities of p-adic integrals from one…