相关论文: The Zariski-Lipman conjecture for log canonical sp…

This note proposes a probabilistic language-free proof of the famous Croot-Laba-Sisask Lemma. In between, we do the same for the Khintchine and Marcinkiewicz-Zygmund inequalities and explicitate the implied constants.

We give an elementary proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves by using Kato's element.

We prove the Remling's Theorem on canonical systems and discuss the connection between Jacobi and Schr\"odinger equation and canonical systems.

Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.

In this paper, I prove a very general extension theorem for log pluricanonical systems. The main application of this extension theorem is (together with Kawamata's subadjunction theorem) to give an optimal subadjunction theorem which…

We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\'ar's gluing theory on lc centers, we prove that the (relative) abundance conjecture for slc pairs is implied by…

In this paper we give a solution to Zariski's problem of analytic classification of plane branches.

We give a new proof of Lucas' Theorem in elementary number theory.

In this paper, we prove that the original Littlewood-Paley $g$-functions can be used to characterize Bergman spaces as well.

We establish adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality.

We prove the Aharoni Berger Conjecture

In this article we determine the implicational fragments of most of the known subintuitionistic logics.

This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.

Inspired by a paper of Salberger we give a new proof of Manin's conjecture for toric varieties over imaginary quadratic number fields by means of universal torsor parameterizations and elementary lattice point counting.

We prove Union-Closed sets conjecture.

We give an elementary proof of a Landesman-Lazer type result for systems by means of a shooting argument and explore its connection with the fundamental theorem of algebra.

We give bounds for the module sectional category of products of maps which generalise a theorem of Jessup for Lusternik-Schnirelmann category. We deduce also a proof of a Ganea type conjecture for topological complexity. This is a first…

We prove the finiteness of $B$-representations of generalised log canonical pairs. As a consequence, we prove that, the (relative) abundance for a generalised semi-log canonical pair is implied by the abundance for its normalisation.…

By the example of the proof of Minkowski's conjecture on critical determinant we give a category theory framework for interval computation.

We describe some results on moduli space of logarithmic connections equipped with framings on a $n$-pointed compact Riemann surface.