Related papers: The Dimension Conjecture Implies The Jacobi Bound …
It is shown that the $n$-dimensional Jacobian conjecture over algebraic number fields may be considered as an existence problem of integral points on affine curves. More specially, if the Jacobian conjecture over $\mathbb{C}$ is false, then…
We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices.
We prove the equivalence of the Jacobian Conjecture (JC(n)) and the Conjecture on the cardinality of the set of fixed points of a polynomial nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n).
We prove a result on lower bounds in large dimensions.
The Jacobian conjecture is an old unsolved problem in mathematics, which has been unsuccessfully attacked from many different angles. We add here another point of view pertaining to the so called formal inverse approach, that of…
The conjecture of Valent about the type of Jacobi matrices with polynomially growing weights is proved.
In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…
It is demonstrated that the knowledge of a single and arbitrary solution of the three-dimension\-al Jacobi equations allows determining infinite families of new solutions, which are generally and explicitly constructed in what follows.…
A result by C. C.-A. Cheng, J. H. Mckay and S. S.-S. Wang says the following: Suppose the Jacobian of $A$ and $B$ is invertible in $\mathbb{C}[x,y]$ and the Jacobian of $A$ and $w$ is zero for $A,B,w \in \mathbb{C}[x,y]$. Then $w \in…
We show that the finitistic dimension conjecture holds for all finite dimensional algebras if and only if, for all finite dimensional algebras, the finitistic dimension of an algebra being finite implies that the finitistic dimension of its…
The Jacobian conjecture involves the map $y= x - V(x)$ where $y, x$ are n-dimensional vectors, $V(x)$ is a symmetric polynomial of degree $d$ for which the Jacobian hypothesis holds: $ e^{Tr \ln(1- V'(x))} =1,\ \forall x$. The conjecture…
A new simple way to prove the Frobenius conjecture on the dimensions of real algebras without zero divisors is given.
We present several versions of the Jacobian Conjecture in positive characteristic each of which if true would imply the Jacobian conjecture in characteristic 0. We test these characteristic p versions of the conjecture against several…
The existence of a "Plastikstufe" for a contact structure implies the Weinstein conjecture for all supporting contact forms.
The finitistic dimension conjecture is closely connected to the symmetry of the finitistic dimension. Recent work indicates that such connection extends to one of its upper bounds, the delooping level. In this paper, we show that the same…
We generalize the property of Jacobi-orthogonality to indefinite scalar product spaces. We compare various principles and investigate relations between Osserman, Jacobi-dual, and Jacobi-orthogonal algebraic curvature tensors. We show that…
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.
We prove that if the Jacobian Conjecture in two variables is false and (P,Q) is a standard minimal pair, then the Newton polygon HH(P) of P must satisfy several restrictions that had not been found previously. This allows us to discard some…
We show that the abc Conjecture implies the Weak Diversity Conjecture of Bilu and Luca.
In 2005, the second author and Todorov introduced an upper bound on the finitistic dimension of an Artin algebra, now known as the {\phi}-dimension. The {\phi}-dimension conjecture states that this upper bound is always finite, a fact that…