Related papers: The Brumer--Stark Conjecture over Z

Using Balmer--Favi's generalized idempotents, we establish the telescope conjecture for many algebraic stacks. Along the way, we classify the thick tensor ideals of perfect complexes of stacks.

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.

The theory of Weil-Stark elements is used to develop an axiomatic approach to the formulation of refined versions of Stark's Conjecture. This gives concrete new results concerning leading terms of Artin $L$-series and arithmetic properties…

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.

Given an abelian, CM extension K of any totally real number field k, we consider two conjectures `of Stark type'. The `Integrality Conjecture' concerns the image of a p-adic map `\mathfrak{s}_{K/k,S}' determined by the minus-part of the…

Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.

We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several…

In this paper, we develop the method of circle of partitions and associated statistics. As an application we prove conditionally the binary Goldbach conjecture. We develop a series of steps to prove the binary Goldbach conjecture in full.…

This paper makes a fundamental assertion about the Erd\H{o}s-Straus conjecture. Suppose that for a prime $p$ there exists $x,y,z \in \mathbb{N}$ with $x \leq y \leq z$ so that $$ \frac{4}{p} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}. $$ The…

This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.

In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We give again (see also arXiv:1112.0676) a proof of weighted estimate of any Calder\'on-Zygmund operator. This is under a universal sharp sufficient condition that is weaker than the so-called bump condition. Bump conjecture was recently…

We show the Graceful Tree Conjecture holds.

We prove Haynes' version of the Duffin--Schaeffer conjecture for the $p$-adic numbers. In addition, we prove several results about an associated related but false conjecture, related to $p$-adic approximation in the spirit of Jarn\'ik and…

We present a proof of the Sturm-Hurwitz theorem, using basic calculus.

We prove explicit upper bounds for weighted sums over prime numbers in arithmetic progressions with slowly varying weight functions. The results generalize the well-known Brun-Titchmarsh inequality.

We propose generalized Fermat's conjecture in the framework of arithmetic dynamics, and give evidences. The multi-indexed version is added.