相关论文: A note on the Artin Conjecture

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

We survey recent developments on the Restriction conjecture.

The purpose of this paper is to put together a large amount of results on the $K(\pi,1)$ conjecture for Artin groups, and to make them accessible to non-experts. Firstly, this is a survey, containing basic definitions, the main results,…

In this paper, we give a survey of the recent develpoments of the DDVV conjecture.

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

New cases of the multiplicity conjecture are considered.

This is a survey on Kawaguchi-Silverman conjecture.

Artin's conjecture is established for all forms that can be realised as a diagonal form on an hyperplane.

We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…

This is an exposition of work on Artin's Conjecture on the zeros of $p$-adic forms. A variety of lines of attack are described, going back to 1945. However there is particular emphasis on recent developments concerning quartic forms on the…

We observe an inductive structure in a large class of Artin groups and exploit this information to deduce the Farrell-Jones isomorphism conjecture for several classes of Artin groups of finite real, complex and affine types.

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

The paper presents a counterexample to the Hodge conjecture.

This is an expanded version of a write-up of a talk given in the fall of 2000 in Oberwolfach. A large part of it is intended to be understandable by non-number theorists with a mathematical background. The talk covered some of the history,…

We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the…

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.

In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

These lecture notes describe the current state of affairs for Manin's conjecture in the context of del Pezzo surfaces.