Related papers: Versions of injectivity and extension theorems
We propose a new approach to the Fourier restriction conjectures. It is based on a discretization of the Fourier extension operators in terms of quadratically modulated wave packets. Using this new point of view, and by combining natural…
A fairly general continuation theorem of Leray-Schauder type for the class of so-called admissible multimaps is set forth. This result is then used to establish a universal rule for solving operator inclusions of Hammerstein type in…
Given a complete K\"ahler manifold $(X,\,\omega)$ with finite second Betti number, a smooth complex hypersurface $Y\subset X$ and a smooth real $d$-closed $(1,\,1)$-form $\alpha$ on $X$ with arbitrary, possibly non-rational, De Rham…
We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the…
We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module…
We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as $\mathbb P^3$ or the quintic threefold. We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth…
We generalize the well-studied notion of a modular pair of a finite matroid to arbitrary families of sets in infinite matroids, and use it to develop the theory of infinite matroids in several as-yet-unexplored areas. Our results include a…
In this note we compare the a-invariant of a homogeneous algebra B to the a-invariant of a subalgebra A. In particular we show that if $A \subset B$ is a finite homogeneous inclusion of standard graded domains over an algebraically closed…
We develop a new approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the…
We extend the minimal model theorem to the 3-dimensional schemes which are projective and have semistable reduction over the spectrum of a Dedekind ring.
We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.
After establishing suitable notions of stability and Chern classes for singular pairs, we use K\"ahler-Einstein metrics with conical and cuspidal singularities to prove the slope semistability of orbifold tangent sheaves of minimal…
We prove a version of faithfully flat descent in rigid analytic geometry, for almost perfect complexes and without finiteness assumptions on the rings involved. This extends results of Drinfeld for vector bundles.
We present a thorough study of the differential geometry of weightings and develop the theory of weightings for vector bundles, Lie groupoids, and Lie algebroids. We begin by extending the work of Loizides and Meinrenken on weighted…
We show injectivity results for assembly maps using equivariant coarse homology theories with transfers. Our method is based on the descent principle and applies to a large class of linear groups or, more general, groups with finite…
A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…
In this expository introductory text we discuss the multiplier ideals in algebraic geometry. We state Kawamata-Viehweg's and Nadel's vanishing theorems, give a proof (following Ein and Lazarsfeld) of Koll\'ar's bound on the maximal…
In this article, we establish an $L^2$ extension theorem for Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles, and the strong openness and stability properties of the multiplier submodule sheaves associated to…
Using Sheaf duality theory of Comer for cylindric algebras, we give a representation theorem of of distributive bounded lattices expanded by modalities (functions distributing over joins) as the continuous sections of sheaves. Our…
In this article we present method of solving some additive problems with primes. The method may be employed to the Goldbach-Euler conjecture and the twin primes conjecture. The presented method also makes it possible to obtain some…