Related papers: On the Cheltsov--Rubinstein conjecture
A proof of Sendov's conjecture is given.
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
In this paper, the abc conjecture is negated under certain conditions
The `Congruence Conjecture' was developed by the second author in a previous paper. It provides a conjectural explicit reciprocity law for a certain element associated to an abelian extension of a totally real number field whose existence…
In this paper, we show that the minimal model theory does not hold in characteristic two. More precisely, we construct counter-examples to the relative abundance conjecture.
In this paper, we prove a conjecture of Schnell in the surface case.
We obtain some new inequalities of Chebyshev Type.
The article presents the proof of Casas-Alvero conjecture.
In this note, making use of noncommutative $l$-adic cohomology, we extend the generalized Riemann hypothesis from the realm of algebraic geometry to the broad setting of geometric noncommutative schemes in the sense of Orlov. As a first…
In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…
The Casas-Alvero conjecture is about interpolation polynomials. There are some partial proofs of it, but there is not any proof in the general case.In this paper we propose three.
A conjecture of Woods from 1972 is disproved.
First, we shall formulate and prove Theorem of Lie-Kolchin type for a cone and derive some algebro-geometric consequences. Next, inspired by a recent result of Dinh and Sibony we pose a conjecture of Tits type for a group of automorphisms…
In this short note we present a family of counterexamples to the King's conjecture.
The purpose of this article is to prove that Gersten's conjecture for a commutative discrete valuation ring is true. Combining with the result of \cite{GL87}, we learn that Gersten's conjecture is true if the ring is a commutative regular…
We show the Williams Conjecture is false for irreducible shifts of finite type by examining relative sign-gyration numbers of conjugacies between shifts with no points of period one or two.
We answer a question that was asked by Albert Baernstein II, regarding the coefficients of circular symmetrization. The conjecture is not true generically.
We prove the Weinstein conjecture for non-trivial contact connected sums under either of two topological conditions: non-trivial fundamental group or torsion-free homology.
We provide new sufficient conditions under which Ryser's conjecture holds.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.