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Artículo
Pierre Deligne
(Real Sociedad Matemática Española, 2013)
Artículo
On the number of rational points on curves over finite fields with many automorphisms
(Elsevier, 2013-01)
Using Weil descent, we give bounds for the number of rational points on two families of curves over finite fields with a large abelian group of automorphisms: Artin–Schreier curves of the form yq−y=f(x) with f∈Fqr[x], on ...
Artículo
Estimates for exponential sums with a large automorphism group
(American Mathematical Society, 2012)
We prove some improvements of the classical Weil bound for one variable additive and multiplicative character sums associated to a polynomial over a finite field k = Fq for two classes of polynomials which are invariant ...
Artículo
Local convolution of l-adic sheaves on the torus
(Springer, 2013-08)
For K and L two l-adic perverse sheaves on the one-dimensional torus Gm,k¯ over the algebraic closure of a finite field, we show that the local monodromies of their convolution K ∗ L at its points of non-smoothness ...
Artículo
Estimates for singular multiplicative character sums
(Duke University Press, 2005)
We give some estimates for multiplicative character sums on quasiprojective varieties over finite fields depending on the severity of the singularities of the variety at infinity. We also remove the hypothesis of ...
Artículo
An Effective Criterion for Finite Monodromy of ℓ-Adic Sheaves
(Springer, 2023-02-01)
We provide an effective version of Katz’ criterion for finiteness of the monodromy group of a lisse, pure of weight zero, -adic sheaf on a normal variety over a finite field, depending on the numerical complexity of the sheaf.
Artículo
Improvements of the Weil bound for Artin-Schreier curves
(Springer, 2011-10)
For the Artin-Schreier curve y q − y = f(x) defined over a finite field Fq of q elements, the celebrated Weil bound for the number of Fq r -rational points can be sharp, especially in super-singular cases and when r is ...
Artículo
Purity of exponential sums on An
(Kluwer, 2006-03)
We give a purity result for two kinds of exponential sums of the type ∑x∈knψ(f(x)), where k is a finite field of characteristic p and ψ:k→C⋆ is a non-trivial additive character. In the first case, f∈k[x1,…,xn] is a polynomial ...
Artículo
Decomposing Jacobians of curves over finite fields in the absence of algebraic structure
(Elsevier, 2015-11)
We consider the issue of when the L-polynomial of one curve over Fq divides the L-polynomial of another curve. We prove a theorem which shows that divisibility follows from a hypothesis that two curves have the same number ...
Artículo
Moment zeta functions for toric Calabi-Yau hypersurfaces
(International Press, 2007)
Moment zeta functions provide a diophantineformulation for the distribution of rational points on afamily of algebraic varieties over finite fields. They also formalgebraic approximations to Dwork’s pp-adic unit rootzeta ...