Related papers: Weak Approximation over Function Fields of Curves …

We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that…

We formulate and prove a weighted version of Zariski's hyperplane section theorem on the topological fundamental groups of the complements of hypersurfaces in a projective space. As an application, we calculate fundamental groups of the…

In this article, we study obstructions to weak approximation for connected linear groups and homogeneous spaces with connected or abelian stabilizers over finite extensions of $\mathbb C((x,y))$ or function fields of curves over $\mathbb…

Let $R$ be the homogeneous coordinate ring of a smooth projective variety $X$ over a field $\k$ of characteristic~0. We calculate the $K$-theory of $R$ in terms of the geometry of the projective embedding of $X$. In particular, if $X$ is a…

In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point…

Let S be a Dedekind scheme with field of functions K. We show that if X_K is a smooth connected proper curve of positive genus over K, then it admits a N\'eron model over S, i.e., a smooth separated model of finite type satisfying the usual…

We propose a linear version of the weighted bounded negativity conjecture. It considers a smooth projective surface $X$ over an algebraically closed field of characteristic zero and predicts the existence of a common lower bound on…

Let $k$ be a field and let $\text{GW}(k)$ be the Grothendieck-Witt ring of virtual non-degenerate symmetric bilinear forms over $k$. We develop methods for computing the quadratic Euler characteristic $\chi(X/k)\in \text{GW}(k)$ for $X$ a…

We give a new proof of the Semistable Reduction Theorem for curves. The main idea is to present a curve $Y$ over a local field $K$ as a finite cover of the projective line $X=\PP^1_K$. By successive blowups (and after replacing $K$ by a…

A weak wild arithmetic quotient singularity arises from the quotient of a smooth arithmetic surface by a finite group action, where the inertia group of a point on a closed characteristic p fiber is a p-group acting with smallest possible…

This note corrects a mistake in Theorem~4.1 of https://doi.org/10.1016/j.aim.2021.107598 (arXiv:1901.03395). The error noted here does not affect any other results of loc. cit. To correct the error, here I prove a more general result…

Let $X$ be a smooth projective curve over a finite field $\mathbb{F}$ with $q$ elements. For $m\geq 1,$ let $X_m$ be the curve $X$ over the finite field $\mathbb{F}_m$, the $m$-th extension of $\mathbb{F}.$ Let $K_n(m)$ be the $K$-group…

Suppose that $C\subset\mathbb P^2$ is a general enough nodal plane curve of degree $>2$, $\nu\colon \hat C\to C$ is its normalization, and $\pi\colon \hat C\to\mathbb P^1$ is a finite morphism simply ramified over the same set of points as…

We deal with a notion of weak binormal and weak principal normal for non-smooth curves of the Euclidean space with finite total curvature and total absolute torsion. By means of piecewise linear methods, we first introduce the analogous…

The purpose of this paper is to study the approximation of vector valued mappings defined on a subset of a normed space. We investigate Korovkin-type conditions under which a given sequence of linear operators becomes a so-called…

Let $K$ be a field of characteristic zero, let $G$ be a connected linear $K$-algebraic group, and let $H$ be a connected closed subgroup of $G$. Let $X_c$ be a smooth compactification of $X=G/H$, and let $Y\overset{}{\longrightarrow}X_c$ be…

We study strong approximation for the intersection of two affine quadrics. As its application, we prove the fibration method for weak approximation over number fields of rank four with nonsplit fibers split by quadratic extensions.

In this paper, we want to study the link between the presence of compact objects with some analytic structure and the global geometry of a weakly complete surface. We begin with a brief survey of some now classic results on the local…

Given a positive integer $p$, we consider $W^{1,p}$-maps from a Euclidean domain of dimension $p+1$ into a closed Riemannian manifold $\mathcal{N}$. The target manifold is required to satisfy suitable topological conditions; in particular,…

We construct the first weakly special surfaces that are not Campana-special, including the complement of the plane curve $x^2y^3 = 1$ in $\mathbb{A}^2$. We prove that the set of $\mathcal{O}_{K,S}$-integral points on this surface is…