Codes from Jacobian surfaces

This paper is concerned with some Algebraic Geometry codes on Jacobians of genus 2 curves. We derive a lower bound for the minimum distance of these codes from an upper "Weil type" bound for the number of rational points on irreducible (possibly singular or non-absolutely irreducible) curves lying on an abelian surface over a finite field

The minimum and maximum number of rational points on jacobian surfaces over finite fields

We give some bounds on the numbers of rational points on abelian varieties and jacobians varieties over finite fields. The main result is that we determine the maximum and minimum number of rational points on jacobians varieties of dimension 2

The characteristic polynomials of abelian varieties of dimensions 4 over finite fields

We describe the set of characteristic polynomials of abelian varieties of dimension 4 over finite fields

D-modules and projective stacks

We study twisted D-modules on the weighted projective stacks. We determine for which values of the twist and the weight the global section functor is an equivalence, thus, proving a version of Beilinson-Bernstein Localisation Theorem.Comment: 22 pages, minor updates to the previous versio

On the Number of Rational Points on Prym Varieties over Finite Fields

International audienceWe give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2

Contribution à l'étude de la végétation steppique du Maroc oriental: Transect Jerrada - Figuig.

Contribution study to the steppique vegetation of Eastern Morocco: Transect Jerrada-Figuig. Mots clés. Maroc oriental, steppe, écologie, Stipa tenacissima. Key words. Eastern Morocco,Steppe, ecologia, Stipa tenacissima

Smooth projective stacks : ample bundles and D-affinity

This thesis is on the study of sheaves of O-modules and D-modules on projective stacks. In chapter 1, a historical perspective is given on the main fidings that have shaped and influenced the study carried out and exposed in this thesis. In chapter 2, the principal definitions and results used in the forthcoming sections are recalled. An appendix is added at the end of this chapter exposing self-containedly why quotient singularities and orbifolds are two equivalent notions. In chapter 3, the property of ampleness of vector bundles on projective stacks is generalised and studied. Basic properties are given; in particular it is proved that weighted projective stacks have ample tangent vector bundle. In chapter 4, D-modules on projective stacks are studied. General conditions on the weights and the shift guaranteeing a weighted projective stack to be D-affine are given. Thus, proving a version of the Beilinson-Bernstein Localisation Theorem. In particular, a weighted projective stack is D-affine if and only if the greatest common divisor of its weights is one. A theorem of Kashiwara is extended to smooth projective stacks, it is shown that the category of D-modules on a smooth closed projective substack [X] is equivalent to the category of D-modules on the ambient smooth projective stack [Y ] supported on [X]

Governance of the relocation of higher education from an information system point of view

Higher education is one of the sectors whose digital transformation has been accelerated due to Covid19. This transformation has enabled universities and colleges to adapt to new modes of distance education, to use modern technological tools, to acquire new skills and to overcome the space-time constraints of traditional education. In this sense, the entire chain of the educational ecosystem has adjusted to a flexible teaching method that has made it possible to streamline the sharing of content between the teaching body and the learning body. In view of this process of change, this article brings new reflections that will make it possible to expand the offer of higher education beyond the borders of the same country. The relocation of diplomas is a form of international scientific and cultural openness and influence for colleges and universities. For a country like Morocco, this type of approaches will promote support for its strategic orientations, contribute to its digital economy and create a dynamic for the development of areas of cooperation and research, particularly in its African context. However, it is essential to govern this relocation well in order to maintain good control of the distance education offer. The treatment of such governance in the light of the opening of information systems will make it possible to better delimit the informational field of this relocation, ensure better strategic alignment and identify the steering indicators to maintain the expected quality

Number of points on abelian and Jacobian varieties over finite fields

We give upper and lower bounds on the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian surfaces.Comment: 28 page