Related papers: Heights of mixed motives
This paper establishes mixed multiplicity formulas concerning the relationship between mixed multiplicities of modules and mixed multiplicities of rings via rank of modules.
We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.
In this paper, we prove a general result computing the number of rational points of bounded height on a projective variety $V$ which is covered by lines. The main technical result used to achieve this is an upper bound on the number of…
We prove several formulas for the distribution of positive roots.
We describe an algorithm for listing all elements of bounded height in a given number field.
This is the Part II of our paper "Height functions for motives". We consider more general period domains and the height functions on more general sets of motives. We also consider the corresponding Hodge theoretic variant of Nevanlinna…
We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular…
Define the height function h(a) = min{k+(ka\mod p): k=1,2,...,p-1} for a = 0,1,...,p-1. It is proved that the height has peaks at p, (p+1)/2, and (p+c)/3, that these peaks occur at a= [p/3], (p-3)/2, (p-1)/2, [2p/3], p-3,p-2, and p-1, and…
In this paper, we propose a new height function for a variety defined over a finitely generated field over Q. For this height function, we will prove Northcott's theorem and Bogomolov's conjecture, so that we can recover the original…
In this note we extend the concept height on projective spaces to that of weighted height on weighted projective spaces and show how such a height can be computed. We prove some of the basic properties of the weighted height and show how it…
We improve upon the upper bounds for the cardinality of the value set of a multivariable polynomial map over a finite field using the polytope of the polynomial. This generalizes earlier bounds only dependent on the degree of a polynomial.
We study the restricted growth function associated with set partitions, and obtain exact formulas for the number of strong records with height one, the total of record heights over set of partitions, and the number of partitions with a…
Let $F$ be a univariate polynomial or rational fraction of degree $d$ defined over a number field. We give bounds from above on the absolute logarithmic Weil height of $F$ in terms of the heights of its values at small integers: we review…
In this paper, we construct an object of the abelian category of mixed Tate motive associated to multiple zeta values. as a consequence, we prove the inequality of the dimension of the vector space generated by multiple zeta values, which…
The Griffiths height of a variation of Hodge structures over a projective curve is defined as the degree of its canonical line bundle, as defined by Griffiths and generalized by Peters to allow bad reduction points. It may be seen as a…
We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.
We introduce the notion of an enriched set, as an abstraction of enriched categories, and a category of enriched sets. The set of enriched sets is itself described as a set enriched over the category of enriched sets. We introduce a method…
We introduce the notion of the boundary motive of a scheme X over a perfect field. By definition, it measures the difference between the motive X and the motive with compact support of X. We develop three tools to compute the boundary…
We consider heights of horizontal irreducible divisors on an arithmetic surface with respect to some hermitian line bundle. We obtain both lower and upper bounds for these heights. The results are different and sometimes stronger that those…
Formal (mixed) Hodge structures FHS are introduced in such a way that the Hodge realization of Deligne's 1-motives extends to a realization from Laumon's 1-motives to formal Hodge structures of level 1, providing an equivalence of…