Related papers: Algebroids and Jacobian conjecture

Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to be equivalent to generalized Lie…

We study the arithmetic of curves and Jacobians endowed with the action of a finite group $G$. This includes a study of the basic properties, as $G$-modules, of their $\ell$-adic representations, Selmer groups, rational points and…

It is well known that the integral identity conjecture is of prime importance in Kontsevich-Soibelman's theory of motivic Donaldson-Thomas invariants for non-commutative Calabi-Yau threfolds. In this article we consider its numerical…

The Jacobi identity is one of the properties that are used to define the concept of Lie algebra and in this context is closely related to associativity. In this paper we provide a complete description of all bivariate polynomials that…

Deligne has conjectured that certain mixed Hodge theoretic invariants of complex algebraic invariants are motivic. This conjecture specializes to an algebraic construction of the Jacobian for smooth projective curves, which was done by A.…

The notion of a generalized Lie bialgebroid (a generalization of the notion of a Lie bialgebroid) is introduced in such a way that a Jacobi manifold has associated a canonical generalized Lie bialgebroid. As a kind of converse, we prove…

In his previous papers (Math. Res. Letters 7 (2000), 123--13; Math. Res. Letters 8 (2001), 429--435; Moscow Math. J. 2 (2002), issue 2, 403-431) the author proved that in characteristic $\ne 2$ the jacobian $J(C)$ of a hyperelliptic curve…

We prove the existence of Euler systems for adjoint modular Galois representations using deformations of Galois representations coming from Hilbert modular forms and relate them to $p$-adic $L$-functions under a conjectural formula for the…

Szmytkowski derived a certain integral with Gegenbauer polynomials. A natural generalization is to derive lookalike integrals with Jacobi polynomials. Six methods are treated to derive the first integral. The first method should be enough…

Jacobson proved that if a Lie algebra admits an invertible derivation, it must be nilpotent. He also suspected, though incorrectly, that the converse might be true: that every nilpotent Lie algebra has an invertible derivation. We prove…

We describe an explicit version of Hilbert's irreducibility theorem using a generalization of Gallagher's larger sieve. We give applications to the Galois theory of random polynomials, and to the images of the adelic representation…

Let $E/F$ be a quadratic extension of p-adic fields. We prove that every smooth irreducible ladder representation of the group $GL_n(E)$ which is contragredient to its own Galois conjugate, possesses the expected distinction properties…

The class-invariant homomorphism allows one to measure the Galois module structure of extensions obtained by dividing points on abelian varieties. In this paper, we consider the case when the abelian variety is the Jacobian of a Fermat…

We describe an algorithm to compute the minimal field of definition of the Tate classes on powers of a Jacobian $J$ with potential complex multiplication. This field arises as a natural invariant of the Galois representations attached to…

Recently the problem of constructing a perfect Euler cuboid was related with three conjectures asserting the irreducibility of some certain three polynomials depending on integer parameters. In this paper a partial result toward proving the…

We consider the Jacobi matrix generated by a balanced measure of hyperbolic polynomial map. The conjecture of Bellissard says that this matrix should have an extremely strong periodicity property. We show how this conjecture is related to a…

Let K[x,y] be the algebra of two-variable polynomials over a field K. A polynomial p=p(x, y) is called a test polynomial (for automorphisms) if, whenever \phi(p)=p for a mapping \phi of K[x,y], this \phi must be an automorphism. Here we…

A central conjecture in inverse Galois theory, proposed by D\`{e}bes and Deschamps, asserts that every finite split embedding problem over an arbitrary field can be regularly solved. We give an unconditional proof of a consequence of this…

Using Jacobian Elliptic functions, we introduce a novel parametrization of a hyperbolic pencil of coaxal circles which reveals a remarkable group structure on the pencil. The geometric properties of the group elements lead to a new proof of…

We discuss the structure of the endomorphism algebras of the jacobians of superelliptic curves y^q=f(x) where q is a prime power and f(x) is an irreducible cubic or quartic polynomial over the field of rational functions k(t) in…