Related papers: A note on the Hodge conjecture
We give a counterexample to the proof in the literature [K-Theory 25 (2002), 215-231] of the existence of linear representatives of higher Chow groups of number fields.
Two conjectures recently proposed by one of the authors are disproved
We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.
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.
In this paper, we exhibit an example of a smooth proper variety in positive characteristic possessing two liftings with different Hodge numbers.
This paper has been withdrawn by the authors
Several results about the union-closed sets conjecture are presented.
This paper is withdrawn. We found a mistake in Lemma 4.1
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.
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.
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
We show that the Jacobian conjecture of the two dimensional case is true.
We give a stack-theoretic proof for some results on families of hyperelliptic curves.
In this paper, we proved a special case of the DDVV Conjecture.
The paper provides a version of the rational Hodge conjecture for $\3\dg$ categories. The noncommutative Hodge conjecture is equivalent to the version proposed in \cite{perry2020integral} for admissible subcategories. We obtain examples of…
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
We show that there is a knot satisfying the property that for each minimal crossing number diagram of the knot and each single crossing of the diagram, changing the crossing results in a diagram for a knot whose unknotting number is at…
In this note we record a comparison theorem on the B-model variation of semi-infinite Hodge structures. This result is considered a folklore theorem by experts in the field. We only take this opportunity to write it down. Our motivation is…
This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.