Related papers: Borel Conjecture and Dual Borel Conjecture
As already noted by Niels Borne and Michel Emsalem, there is a natural generalization of the section conjecture for proper orbicurves. Combined with the reformulation by Niels Borne and Angelo Vistoli of the conjecture in terms of the…
We show that the Dual Borel Conjecture implies that ${\mathfrak d}> \aleph_1$ and find some topological characterizations of perfectly meager and universally meager sets.
This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.
In this paper, we will give an extension of Mok's theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.
We give an equivalent form of the Twin prime conjecture relating to a symmetric property that is observed for terms present in a certain sequence of arithmetic progressions defined for a pair of co-prime integers.
Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.
We prove in this paper the Ax-Schanuel conjecture for all admissible variations of mixed Hodge structures.
Turner's Conjecture describes all blocks of symmetric groups and Hecke algebras up to derived equivalence in terms of certain double algebras. With a view towards a proof of this conjecture, we develop a general theory of Turner doubles. In…
We give a version of the Borel-Cantelli lemma. As an application, we prove an almost sure local central limit theorem. As another application, we prove a dynamical Borel-Cantelli lemma for systems with sufficiently fast decay of…
I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the…
General considerations on the Equivalence conjectures and a review of few mathematical results.
We prove The Tate Thomason conjecture through Theorem 2.2. Fundamental is the work of R W Thomson and the proof also rests upon the theory of infinite abelian groups.
We prove the dynamical Mordell-Lang conjecture for birational polynomial morphisms on $\mathbb{A}^2$.
We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.
In this paper, we proved a special case of the DDVV Conjecture.
In this paper we first consider hyperfinite Borel equivalence relations with a pair of Borel $\mathbb{Z}$-orderings. We define a notion of compatibility between such pairs, and prove a dichotomy theorem which characterizes exactly when a…
We prove under some assumptions that the Tate conjecture holds for products of Fermat varieties of different degrees.
The aim of this work is to prove a conjecture related to the Combinatorial Invariance Conjecture of Kazhdan-Lusztig polynomials, in the parabolic setting, for lower intervals in every arbitrary Coxeter group. This result improves and…