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Browsing by Author "Rojas León, Antonio"
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7o Congreso Europeo de Matemáticas [Article]
Rojas León, Antonio (Real Sociedad Matemática Española, 2016)La séptima edición del Congreso Europeo de Matemáticas, evento que tiene lugar cada cuatro años bajo los auspicios de la Sociedad Matemática Europea, se celebró entre los pasados días 18 y 22 de julio en la sede de la ...

A rigid local system with monodromy group 2.J2 [Article]
Katz, Nicholas M.; Rojas León, Antonio (Elsevier, 201905)We exhibit a rigid local system of rank six on the affine line in characteristic p = 5 whose arithmetic and geometric monodromy groups are the finite group 2.J2 (J2 the HallJanko sporadic group) in one of its two ...

Continuous division of linear differential operators and faithful flatness of D∞X over DX [Article]
Narváez Macarro, Luis; Rojas León, Antonio (Société Mathématique de France, 2004)In these notes we prove the faithful flatness of the sheaf of infinite order linear differential operators over the sheaf of finite order linear differential operators on a complex analytic manifold. We give the ...

DMódulos algebraicos y cohomología de familias de Dwork [PhD Thesis]
Castaño Domínguez, Alberto (20140715)Una familia de Dwork es una deformación monomial uniparamétrica de una hipersuperficie de Fermat. Debido a su conexión con las funciones L de sumas de Kloosterman y la simetría espejo, entre otras aplicaciones, resultaría ...

Decomposing Jacobians of curves over finite fields in the absence of algebraic structure [Article]
Ahmadi, Omran; McGuire, Gary; Rojas León, Antonio (Elsevier, 201511)We consider the issue of when the Lpolynomial of one curve over Fq divides the Lpolynomial of another curve. We prove a theorem which shows that divisibility follows from a hypothesis that two curves have the same number ...

Dominios de Dedekind, factorización de ideales y aplicaciones [Final Degree Work]
Daza Garcia, Alberto (20180620)In order to study some number theoretical problems, algebraic number fields and their ring of integers have being introduced. In this dissertation rings of integers and their arithmetic properties will be studied. Since ...

Estimates for exponential sums with a large automorphism group [Article]
Rojas León, Antonio (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 ...

Estimates for singular multiplicative character sums [Article]
Rojas León, Antonio (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 ...

Explicit local multiplicative convolution of ℓadic sheaves [Article]
Rojas León, Antonio (European Mathematical Society, 2018)We give explicit formulas for the local multiplicative convolution functors, which express the local monodromies of the convolution of two ℓadic sheaves on the torus Gm over the algebraic closure of a finite field in terms ...

Finite monodromy of some families of exponential sums [Article]
Rojas León, Antonio (Elsevier, 201904)Given a prime p and an integer d > 1, we give a numerical criterion to decide whether the ℓadic sheaf associated to the oneparameter exponential sums t 7→P x ψ(xd + tx) over Fp has finite monodromy or not, and work ...

Improvements of the Weil bound for ArtinSchreier curves [Article]
Rojas León, Antonio; Wan, Daqing (Springer, 201110)For the ArtinSchreier 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 supersingular cases and when r is ...

KatzRadon transform of ladic representations [Article]
Rojas León, Antonio (Duke University Press, 2012)We prove a simple explicit formula for the local KatzRadon transform of an ladic representation of the Galois group of the fraction field of a strictly henselian discrete valuation ring with positive residual characteristic, ...

Lfunctions of symmetric powers of the generalized Airy family of exponential sums [Article]
Haessig, C. Douglas; Rojas León, Antonio (201112)This paper looks at the Lfunction of the kth symmetric power of the sheaf Aif over the affine line associated to the generalized Airy family of exponential sums. Using ℓadic techniques, we compute the degree of this ...

Local convolution of ladic sheaves on the torus [Article]
Rojas León, Antonio (Springer, 201308)For K and L two ladic perverse sheaves on the onedimensional 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 nonsmoothness ...

Mesa Redonda «Investigación: Presente y Futuro», Granada, 6 de febrero de 2015 [Article]
Rodríguez Pérez, Magdalena; Rojas León, Antonio (Real Sociedad Matemática Española, 2015) 
Moment zeta functions for toric CalabiYau hypersurfaces [Article]
Rojas León, Antonio; Wan, Daqing (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 ppadic unit rootzeta ...

On the number of rational points on curves over finite fields with many automorphisms [Article]
Rojas León, Antonio (Elsevier, 201301)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 ...

Pierre Deligne [Article]
Rojas León, Antonio (Real Sociedad Matemática Española, 2013) 
Purity of exponential sums on An [Article]
Rojas León, Antonio (Kluwer, 200603)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 nontrivial additive character. In the first case, f∈k[x1,…,xn] is a polynomial ...

Purity of exponential sums on An, II [Article]
Rojas León, Antonio (De Gruyer, 200703)We give a purity result for exponential sums of the type P x∈kn ψ(f(x)), where k is a finite field of characteristic p, ψ : k → C* is a nontrivial additive character and f ∈ k[x1, . . . , xn] is a polynomial whose highest ...