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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
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
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
L-functions of symmetric powers of the generalized Airy family of exponential sums
(2011-12)
This paper looks at the L-function of the kth symmetric power of the -sheaf Aif over the affine line associated to the generalized Airy family of exponential sums. Using ℓ-adic techniques, we compute the degree of this ...
Artículo
Katz-Radon transform of l-adic representations
(Duke University Press, 2012)
We prove a simple explicit formula for the local Katz-Radon transform of an l-adic representation of the Galois group of the fraction field of a strictly henselian discrete valuation ring with positive residual characteristic, ...
Artículo
Explicit local multiplicative convolution of ℓ-adic sheaves
(European Mathematical Society, 2018)
We give explicit formulas for the local multiplicative convolution functors, which express the local monodromies of the convolution of two ℓ-adic sheaves on the torus Gm over the algebraic closure of a finite field in terms ...
Artículo
A rigid local system with monodromy group 2.J2
(Elsevier, 2019-05)
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 Hall-Janko sporadic group) in one of its two ...