Results 1 to 10 of about 339 (22)

Noninjectivity of the cycle class map in continuous $\ell $ -adic cohomology

Forum of Mathematics, Sigma, 2023
Jannsen asked whether the rational cycle class map in continuous $\ell $ -adic cohomology is injective, in every codimension for all smooth projective varieties over a field of finite type over the prime field. As recently pointed out by Schreieder,
Federico Scavia, Fumiaki Suzuki
doaj   +1 more source

Heights on stacks and a generalized Batyrev–Manin–Malle conjecture

Forum of Mathematics, Sigma, 2023
We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual notion for rational points on projective varieties.
Jordan S. Ellenberg, Matthew Satriano, David Zureick-Brown   +2 more
doaj   +1 more source

Arithmetic hyperbolicity and a stacky Chevalley–Weil theorem

Journal of the London Mathematical Society, Volume 103, Issue 3, Page 846-869, April 2021., 2021
Abstract We prove an analogue for algebraic stacks of Hermite–Minkowski's finiteness theorem from algebraic number theory, and establish a Chevalley–Weil type theorem for integral points on stacks. As an application of our results, we prove analogues of the Shafarevich conjecture for some surfaces of general type.
Ariyan Javanpeykar, Daniel Loughran
wiley   +1 more source

RATIONAL CURVES ON CUBIC HYPERSURFACES OVER FINITE FIELDS

Mathematika, Volume 67, Issue 2, Page 366-387, April 2021., 2021
Abstract Given a smooth cubic hypersurface X over a finite field of characteristic greater than 3 and two generic points on X, we use a function field analogue of the Hardy–Littlewood circle method to obtain an asymptotic formula for the number of degree d k‐rational curves on X passing through those two points.
Adelina Mânzăţeanu
wiley   +1 more source

Multivariable polynomial injections on rational numbers [PDF]

, 2010
For each number field k, the Bombieri-Lang conjecture for k-rational points on surfaces of general type implies the existence of a polynomial f(x,y) in k[x,y] inducing an injection k x k --> k.Comment: 4 ...
Poonen, Bjorn
core   +3 more sources

Failure of strong approximation on an affine cone [PDF]

, 2018
We use the Brauer-Manin obstruction to strong approximation on a punctured affine cone to explain a curious property of coprime integer solutions to a homogeneous Diophantine equation.Comment: Changes following referee's ...
Bright, Martin, Kok, Ivo
core   +3 more sources

The Picard group of Brauer-Severi varieties

Open Mathematics, 2018
In this paper, we provide explicit generators for the Picard groups of cyclic Brauer-Severi varieties defined over the base field. In particular,we provide such generators for all Brauer-Severi surfaces.
Badr Eslam, Bars Francesc, García Elisa Lorenzo   +2 more
doaj   +1 more source

The density of zeros of forms for which weak approximation fails [PDF]

, 1992
The weak approximation principal fails for the forms x3 + y3 + z3 = kw3, when k = 2 or 3. The question therefore arises as to what asymptotic density one should predict for the rational zeros of these forms.
Heath-Brown, D. R.
core   +1 more source

Local Euler characteristics of $A_n$-singularities and their application to hyperbolicity [PDF]

Épijournal de Géométrie Algébrique
Wahl's local Euler characteristic measures the local contributions of a singularity to the usual Euler characteristic of a sheaf. Using tools from toric geometry, we study the local Euler characteristic of sheaves of symmetric differentials for isolated ...
Nils Bruin, Nathan Ilten, Zhe Xu
doaj   +1 more source

Characteristic ideals and Selmer groups [PDF]

, 2014
Let $A$ be an abelian variety defined over a global field $F$ of positive characteristic $p$ and let $\calf/F$ be a $\Z_p^{\N}$-extension, unramified outside a finite set of places of $F$. Assuming that all ramified places are totally ramified, we define
Bandini, Andrea, Bars, Francesc, Longhi, Ignazio   +2 more
core   +4 more sources