Related papers: A Counter Example To the Hodge Conjecture

The paper presents a counterexample to the Hodge conjecture.

In this short note we present a family of counterexamples to the King's conjecture.

We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

The Hodge conjecture is a major open problem in complex algebraic geometry. In this survey, we discuss the main cases where the conjecture is known, and also explain an approach by Griffiths-Green to solve the problem.

This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

The Hodge conjecture is shown to be equivalent to a question about the homology of very ample divisors with ordinary double point singularities. The infinitesimal version of the result is also discussed.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

A conjecture of Woods from 1972 is disproved.

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

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.

In this short note,we correct a well-known counter example of the famous book of Dacorogna[2].

In this paper, the abc conjecture is negated under certain conditions

In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.

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 consider the remaining cases of Hebey-Vaugon conjecture.

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…

In this paper we show the equivalence of the conjectures of Giuga and Agoh in a direct way which leads to a combined conjecture. This conjecture is described by a sum of fractions from which all conditions can be derived easily.