Results 11 to 20 of about 323 (40)
Value sets of sparse polynomials [PDF]
, 2018 We obtain a new lower bound on the size of value set f(F_p) of a sparse polynomial f in F_p[X] over a finite field of p elements when p is prime. This bound is uniform with respect of the degree and depends on some natural arithmetic properties of the ...
Shparlinski, Igor E. +1 more
core +2 more sources
The probability that a complete intersection is smooth [PDF]
, 2012 Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is smooth of the expected dimension.
Bucur, Alina, Kedlaya, Kiran S.
core +2 more sources
Curves, dynamical systems and weighted point counting [PDF]
, 2012 Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k. Counting the number of points on X over all finite field extensions of k will not determine the curve uniquely. Actually, a famous theorem of Tate implies that two such
Cornelissen, Gunther
core +1 more source
The characteristic polynomials of abelian varieties of dimensions 4 over finite fields [PDF]
, 2010 We describe the set of characteristic polynomials of abelian varieties of dimension 4 over finite ...
Haloui, Safia, Singh, Vijaykumar
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Toward a geometric analogue of Dirichlet's unit theorem [PDF]
, 2014 In this note, we propose a geometric analogue of Dirichlet's unit theorem on arithmetic varieties, that is, if X is a normal projective variety over a finite field and D is a pseudo-effective Q-Cartier divisor on X, does it follow that D is Q-effective ...
Moriwaki, Atsushi
core +3 more sources
Vanishing Ideals Over Odd Cycles
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 Let K be a finite field. Let X* be a subset of the a ne space Kn, which is parameterized by odd cycles. In this paper we give an explicit Gröbner basis for the vanishing ideal, I(X*), of X*.
Uribe-Paczka M. Eduardo +2 more
doaj +1 more source
Rational points on certain hyperelliptic curves over finite fields
, 2007 Let $K$ be a field, $a, b\in K$ and $ab\neq 0$. Let us consider the polynomials $g_{1}(x)=x^n+ax+b, g_{2}(x)=x^n+ax^2+bx$, where $n$ is a fixed positive integer.
Ulas, Maciej
core +1 more source
On the cyclicity of the rational points group of abelian varieties over finite fields
, 2018 We propose a simple criterion to know if an abelian variety $A$ defined over a finite field $\mathbb{F}_q$ is cyclic, i.e., it has a cyclic group of rational points; this criterion is based on the endomorphism ring End$_{\mathbb{F}_q}(A)$.
Giangreco-Maidana, Alejandro J.
core +3 more sources
An application of random plane slicing to counting $\mathbb{F}_q$-points on hypersurfaces
, 2019 Let $X$ be an absolutely irreducible hypersurface of degree $d$ in $\mathbb{A}^n$, defined over a finite field $\mathbb{F}_q$. The Lang-Weil bound gives an interval that contains $#X(\mathbb{F}_q)$. We exhibit explicit intervals, which do not contain $#X(
Slavov, Kaloyan
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The structure of Deitmar Schemes, II. Zeta functions and automorphism groups [PDF]
, 2016 We provide a coherent overview of a number of recent results obtained by the authors in the theory of schemes defined over the field with one element.
Merida-Angulo, Manuel, Thas, Koen
core +1 more source