Related papers: A note on the Hodge conjecture

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…

In this paper we discuss an obstruction to the integral Hodge conjecture, which arises from certain behavior of vanishing cycles. This allows us to construct new counter-examples to the integral Hodge conjecture. One typical such…

In this paper, we prove a conjecture of Schnell in the surface case.

A proof of Sendov's conjecture is given.

In this note we give a counterexample to a conjecture proposed by Ciliberto about special linear systems of P^n through multiple base points.

The present note sketches a theory of constructs.

In this note we prove a weighted version of the Khintchine inequalities.

It is shown that Darwiche and Pearl's postulates imply an interesting property, not noticed by the authors.

After reconsidering the Dasbach-Hougardy counterexample to the Kauffman Conjecture on alternating knots, we reformulate the conjecture and consider Dasbach-Hougardy counterexample and similar counterexamples in the light of the reformulated…

The note complements topological aspects of the theory of chiral algebras.

We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.

We study the integral Hodge conjecture in complex codimension $2$ and $3$ for approximations to the classifying space of groups of type A. In degree two, we prove a conjecture of Ben Antieau, extending his two counterexamples to a general…

We give a minimal counterexample for a conjecture of Ross and Yong (2015) which proposes a K-Kohnert rule for Grothendieck polynomials. We conjecture a revised version of this rule. We then prove both rules hold in the $321$-avoiding case.

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We give a visually appealing counterexample to the proposition that unbiased estimators are better than biased estimators.

The purpose of this note is to give counterexamples to the containment $I^{(3)}\subset I^2$ over the real numbers.

In this paper we give an example to show Clemens' conjecture is not a first order deformation problem.

An technically interesting proof of a known theorem.

We provide a counter-example to Proposition 3.2 of "A note on the Fundamental Group of a Triangular Algebra", by F.Xu.

In this note, we derive a Leibniz rule for difference quotient.