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

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 characteristic polynomials of abelian varieties of dimensions 3 over finite fields

We describe the set of characteristic polynomials of abelian varieties of dimension 3 over finite fields

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

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]

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

0241 : Does Ramadan fasting has any effects on hemoglobin, glucose and renal function in patients with chronic heart failure?

ObjectiveThe effects of Islamic fasting on physiologic functions in normal conditions have been considered in different studies and different topics. This study was to determine the quantitative changes of hemoglobin, glucose and renal function during Ramadan fasting in patients with chronic heart failure.MethodsFifty-three outpatients with chronic heart failure were followed in 2 stages: one week before the start of Ramadan and then on the last day of Ramadan by proper blood sampling in suitable time of day.ResultsThere were 31 (58.5%) males and 22 (41.5%) females with a mean age of 60±11.06 years. Nineteen patients (35.8%) had mild left ventricular systolic dysfunction, 29 patients (54.7%) had moderate systolic dysfunction and 5 patients (9.4%) had severe systolic dysfunction. There were no significant changes in the NYHA Class nor there were any significant changes in the Canadian Cardiac Society (CCS) class in patients with coronary artery disease. We found non significant decrease in hemoglobin and blood glucose level (P=0.76) and (P=0.16) respectively, and non significant increase in creatinine (P=0.07) before and at the end of Ramadan in either males or females.ConclusionThe conclusions from this study can not be extrapolated to patients with worse functional classes or those who are unstable. It is clear that more work should be carried out to evaluate the impact of fasting on cardiac patients with higher NYHA class, and discover the significance of Ramadan fasting in patients with heart disease

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