Related papers: About the Proof of Lang's Height Conjecture

We discuss the connection between the smooth and metric structure on quotient spaces, prove smoothness of isometries in special cases and discuss an application to a conjecture of Molino.

Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant C such that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at most one…

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

We prove effective versions of algebraic and analytic Lang's conjectures for product-quotient surfaces of general type with $P_g=0$ and $c_1^2=c_2$.

In this paper I verify Manin's conjecture for a class of rational projective toric varieties with a large class of heights other than the usual one that comes from the standard metric on projective space.

We outline some recent proofs of quantum ergodicity on large graphs and give new applications in the context of irregular graphs. We also discuss some remaining questions.

We discuss historical attempts to formulate a physical hypothesis from which Turing's thesis may be derived, and also discuss some related attempts to establish the computability of mathematical models in physics. We show that these…

I give a simplified proof of one of the main results in the recent preprint arXiv:1311.5858 by X. Luo and K. Zuo. Furthermore, I discuss the relation with the Coleman-Oort conjecture on special curves in the Torelli locus.

Nous rappelons l'historique de la demonstration de la conjecture des fibres de Seifert, ainsi que ses motivations et ses diverses generalisations. ----- We recall the history of the proof of the Seibert fiber space conjecture, as well as…

Let E be an elliptic curve with additive reduction over the p-adic numbers, and let G be the group of p-adic points on E that have good reduction. This paper gives necessary and sufficient conditions for G to contain non-trivial p-torsion.

Given a euclidean lattice and a curve in the corresponding projective space, our goal is to relate the height of the curve to the successive minima of the lattice. The proof of such a statement in http://hal.archves-ouvertes.vf/hal-00270564…

We present a formal measure of argument strength, which combines the ideas that conclusions of strong arguments are (i) highly probable and (ii) their uncertainty is relatively precise. Likewise, arguments are weak when their conclusion…

We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures would lead to a deeper understanding of the Willmore functional…

This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].

Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.

The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.

In this paper, we give a simple counter example to the famous Hodge conjecture.

The aim of this paper is to introduce a new family of elliptic curves with positive ranks. These elliptic curves have been constructed with certain rational numbers, namely a, b, and c as sides of Heron triangles having rational areas $k$.…

We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…