✦ LIBER ✦

Modular Counting of Rational Points over Finite Fields

✍ Scribed by Daqing Wan

Publisher: Springer-Verlag
Year: 2007
Tongue: English
Weight: 251 KB
Volume: 8
Category: Article
ISSN: 1615-3375
DOI: 10.1007/s10208-007-0245-y

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

On Drinfeld Modular Curves with Many Rat

On Drinfeld Modular Curves with Many Rational Points over Finite Fields

✍ Andreas Schweizer 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 137 KB

It is known that Drinfeld modular curves can be used to construct asymptotically optimal towers of curves over finite fields. Using reductions of the Drinfeld modular curves X 0 ðnÞ, we try to find individual curves over finite fields with many rational points. The main idea is to divide by an Atkin

Counting Points on Curves over Finite Fi

Counting Points on Curves over Finite Fields

✍ Ming-Deh Huang; Doug Ierardi 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 602 KB

We consider the problem of counting the number of points on a plane curve, defined by a homogeneous polynomial F (x, y, z) ∈ Fq[x, y, z], which are rational over a ground field Fq. More precisely, we show that if we are given a projective plane curve C of degree n, and if C has only ordinary multipl

Equivariant Poincaré Polynomials and Cou

Equivariant Poincaré Polynomials and Counting Points over Finite Fields

✍ M. Kisin; G.I. Lehrer 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 139 KB

Suppose a finite group acts as a group of automorphisms of a smooth complex algebraic variety which is defined over a number field. We show how, in certain circumstances, an equivariant comparison theorem in l-adic cohomology may be used to convert the computation of the graded character of the indu

Congruences for rational points on varie

Congruences for rational points on varieties over finite fields

✍ N. Fakhruddin; C. S. Rajan 📂 Article 📅 2005 🏛 Springer 🌐 English ⚖ 180 KB

Counting Points on Curves and Abelian Va

Counting Points on Curves and Abelian Varieties Over Finite Fields

✍ Leonard M. Adleman; Ming-Deh Huang 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 343 KB

We develop efficient methods for deterministic computations with semi-algebraic sets and apply them to the problem of counting points on curves and Abelian varieties over finite fields. For Abelian varieties of dimension g in projective N space over Fq, we improve Pila's result and show that the pro

On Kummer covers with many rational poin

On Kummer covers with many rational points over finite fields

✍ Arnaldo Garcia; Alvaro Garzon 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 190 KB

We give a simple and e ective method for the construction of algebraic curves over ÿnite ÿelds with many rational points. The curves constructed are Kummer covers or ÿbre products of Kummer covers of the projective line.