Results 1 to 10 of about 33 (33)
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
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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 +2 more
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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
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 +2 more
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Local Euler characteristics of $A_n$-singularities and their application to hyperbolicity [PDF]
Épijournal de Géométrie AlgébriqueWahl'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
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The Manin–Peyre conjecture for smooth spherical Fano varieties of semisimple rank one
Forum of Mathematics, SigmaThe Manin–Peyre conjecture is established for a class of smooth spherical Fano varieties of semisimple rank one. This includes all smooth spherical Fano threefolds of type T as well as some higher-dimensional smooth spherical Fano varieties.
Valentin Blomer +3 more
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Average Analytic Ranks of Elliptic Curves over Number Fields
Forum of Mathematics, SigmaWe give a conditional bound for the average analytic rank of elliptic curves over an arbitrary number field. In particular, under the assumptions that all elliptic curves over a number field K are modular and have L-functions which satisfy the ...
Tristan Phillips
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Improvements on dimension growth results and effective Hilbert’s irreducibility theorem
Forum of Mathematics, SigmaWe sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree d, over any global field.
Raf Cluckers +4 more
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Distinguished liftings and the André-Oort conjecture
, 2002 In this paper we study liftings of affine varieties from finite fields to number fields, such that the lifted varieties contain specified “canonical” lifts of points.
Breuer, Florian
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