Related papers: Note on a differential algebra bound

Given a logarithmic $1$-form on the snc locus of a log canonical surface pair $(X, D)$ over a perfect field of characteristic $p \ge 7$, we show that it extends with at worst logarithmic poles to any resolution of singularities. We also…

This work presents a range of triangulated characterizations for important classes of singularities such as derived splinters, rational singularities, and Du Bois singularities. An invariant called 'level' in a triangulated category can be…

Let $M_k^\sharp(N)$ be the space of weakly holomorphic modular forms for $\Gamma_0(N)$ that are holomorphic at all cusps except possibly at $\infty$. We study a canonical basis for $M_k^\sharp(2)$ and $M_k^\sharp(3)$ and prove that almost…

In this paper we study nonlocal nonlinear equations of fractional $(s,p)$-Laplacian type on $\mathbf{R}^n$. We show that the irregular boundary points for the Dirichlet problem can be divided into two disjoint classes: semiregular and…

Let k be an uncountable field of characteristic different from two. We show that a very general hypersurface of dimension N>2 and degree at least $\log_2N +2$ is not stably rational over the algebraic closure of k.

We establish analogs of sharp weighted weak-type bounds for $m$-sublinear operators satisfying sparse form domination, including multilinear Calder\'on-Zygmund singular integrals. Our results, which hold for general $\vec{p} \in…

Let p=tp(a/A) be a stationary type in an arbitrary finite rank stable theory, and P an A-invariant family of partial types. The following property is introduced and characterised: whenever c is definable over (A,a) and a is not algebraic…

In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to the $p(x)-$Laplacian $$ -\mbox{div}(|\nabla u|^{p(x)-2}\nabla u)+u\in -[\underline{g}(x,u),\overline{g}(x,u)], $$ by using the…

We produce a new family of polynomials f(x) over fields K of characteristic 2 which are exceptional, in the sense that f(x)-f(y) has no absolutely irreducible factors in K[x,y] besides the scalar multiples of x-y; when K is finite, this…

The topology of the matching complex for the $2\times n$ grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes $\mathrm{Ind}(\Delta_n^m)$ that include these matching complexes. Using this…

We consider nonlinear elliptic equations of the $p$-Laplacian type with lower order terms which involve nonnegative potentials satisfying a reverse H\"older type condition. Then we obtain interior and boundary $L^q$ estimates for the…

In this article, we firstly study the cone Moser-Trudinger inequalities and their best exponents $\alpha_2$ on both bounded and unbounded domains $\mathbb{R}^2_{+}$. Then, using the cone Moser-Trudinger inequalities, we study the existence…

The main result of this paper is to prove that if a (right) Leibniz algebra $L$ is \textit{right nilpotent} of degree $n$, then $L$ is \textit{strongly nilpotent} of degree less or equal to $4n^2-2n+1$.

Let $k$ be a field and let $G$ be an affine algebraic group over $k$. Call a $G$-torsor weakly versal for a class of $k$-schemes $\cal C$ if it specializes to every $G$-torsor over a scheme in $\cal C$. A recent result of the first author,…

A sharply 2-transitive permutation group of finite Morley rank and characteristic 2 splits; a split sharply 2-transitive permutation group of finite Morley rank and characteristic different from 2 is the group of affine transformations of…

In this paper, we give a partial affirmative answer to the BAB conjecture for $3$-folds in characteristic $p>5$. Specifically, we prove that a set $\mathcal{D}$ of weak Fano $3$-folds over an uncountable algebraically closed field is…

This paper is the second in a series investigating cartesian closed varieties. In first of these, we showed that every non-degenerate finitary cartesian variety is a variety of sets equipped with an action by a Boolean algebra B and a…

A convergence theorem for martingales with c\`adl\`ag trajectories (right continuous with left limits everywhere) is obtained in the sense of the weak dual topology on Hilbert space, under conditions that are much weaker than those required…

We prove a parabolic analogue of Wolff's inequality adapted to the intrinsic scaling $\delta_c(x,t)=(cx,c^2t)$ and formulated in terms of time-backward parabolic dyadic rectangles. As a consequence, we obtain equivalent characterizations of…

We consider parabolic Schr\"odinger type equations associated to fractional powers of uniformly elliptic 2m-order operators with constant coefficients. Potentials and initial data are considered in suitable Morrey spaces. By means of…