Related papers: A Counter Example To the Hodge Conjecture
We obtain examples of smooth projective varieties over $\mathbb{C}$ that violate the integral Hodge conjecture and for which the total Chow group is of finite rank. Moreover, we show that there exist such examples defined over number…
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…
We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.
We give a proof of some small weight and level cases of Serre's conjecture.
In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…
We survey recent developments on the Restriction conjecture.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
The Jacobian Conjecture has been reduced to the symmetric homogeneous case. In this paper we give an inversion formula for the symmetric case and relate it to a combinatoric structure called the Grossman-Larson Algebra. We use these tools…
We give a visually appealing counterexample to the proposition that unbiased estimators are better than biased estimators.
I present a simple derivation of the de Gennes narrowing phenomenon.
We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.
In this article we derive a simple twisted relative trace formula.
We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionistically equivalent to the usual ones.
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
We obtain a system of relations between linear Hodge integrals. As an application, we show that its first non-trivial relation implies the Witten's Conjecture/Kontsevich Theorem.
General considerations on the Equivalence conjectures and a review of few mathematical results.
We define the category of \'etale Chow motives as the \'etale analogue of Grothendieck motives and proved that it embeds in $\text{DM}_{\text{\'et}}(k)$. This construction provides a characterization of the generalized Hodge conjecture in…
In this paper we present an example of a simple study of velocity proportional resistance force. Some experimental determinations are presented.