Related papers: A note on the Hodge conjecture

In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

The goal of this note is to affirm a local version of the conjecture of Nisse--Sottile [NS16] on higher convexity of complements of tropical varieties, while providing a family of counter-examples for the global Nisse--Sottle conjecture in…

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

In this paper, we present a minimal counterexample to a conjecture of Perles that answers a question of Haase and Ziegler. The example is a simple 4-polytope that has an induced 3-connected 3-regular subgraph, whose graph complement is…

We describe in some details an idea of M. Kontsevich how one can try to find a counterexample to the Hodge conjecture using tropical geometry.

We give a sketch for an alternative proof of a recent result by J. Tseng.

We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.

Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.

A counter example to the main result has been communicated to the author by Matei Toma.

In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.

We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.

This paper has been withdrawn.

This paper has been withdrawn.

A conjecture of Hopkins (2018) posits that for certain high-dimensional hypothesis testing problems, no polynomial-time algorithm can outperform so-called "simple statistics", which are low-degree polynomials in the data. This conjecture…

In this note, we discuss recently discovered counterexamples to Mordell's Pellian Equation Conjecture and the Ankeny-Artin-Chowla-Conjecture. We provide a verification of the counterexample to Mordell's Pellian Equation Conjecture that can…

Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…

We prove the Aharoni Berger Conjecture

We prove Union-Closed sets conjecture.

We prove Burkholder inequality using Bregman divergence.