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Improved upper bounds for the number of points on curves over finite fields

Everett W. Howe, Kristin E. Lauter (2003)

Annales de l’institut Fourier

We give new arguments that improve the known upper bounds on the maximal number $N_{q} (g)$ of rational points of a curve of genus $g$ over a finite field $𝔽_{q}$ , for a number of pairs $(q, g)$ . Given a pair $(q, g)$ and an integer $N$ , we determine the possible zeta functions of genus- $g$ curves over $𝔽_{q}$ with $N$ points, and then deduce properties of the curves from their zeta functions. In many cases we can show that a genus- $g$ curve over $𝔽_{q}$ with $N$ points must have a low-degree map to another curve over $𝔽_{q}$ , and often this is enough to...

Intégration motivique sur les schémas formels

Julien Sebag (2004)

Bulletin de la Société Mathématique de France

Nous généralisons la théorie de l’intégration motivique au cadre des schémas formels. Nous définissons et étudions l’anneau booléen des ensembles mesurables, la mesure motivique, l’intégrale motivique et nous démontrons un théorème de changement de variables pour cette intégrale.

Displaying 1 – 8 of 8

Improved upper bounds for the number of points on curves over finite fields

Intégration motivique sur les schémas formels

Interaction sums and action of Hecke operators on theta-series

Introduction aux travaux de Dwork

Invariant differentials and $L$ -functions. Reciprocity law for quadratic fields and elliptic curves over $𝐐$

Iwasawa L-Functions of Varieties over Algebraic Number Fields.

Iwasawa theory for the symmetric square of an elliptic curve.

Iwasawa-theory of abelian varieties at primes of non-ordinary reduction.

Currently displaying 1 – 8 of 8