POINT COUNTING ON CURVES USING A GONALITY PRESERVING LIFT

被引：3

作者：

Castryck, Wouter ^{[1
,2
,3
]}

Tuitman, Jan ^{[4
]}

机构：

[1] Univ Lille 1, Lab Painleve, F-59655 Villeneuve Dascq, France

[2] Katholieke Univ Leuven, Dept Elektrotech, Kasteelpk Arenberg 10-2452, B-3001 Leuven, Belgium

[3] Imec Cos, Kasteelpk Arenberg 10-2452, B-3001 Leuven, Belgium

[4] Katholieke Univ Leuven, Dept Wiskunde, Celestijnenlaan 200B, B-3001 Leuven, Belgium

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2018年 / 69卷 / 01期

基金：

欧洲研究理事会;

关键词：

KEDLAYAS ALGORITHM; CANONICAL CURVES; LINEAR PENCILS; EXTENSION; PARAMETRIZATION; FAMILIES; SYSTEM;

D O I：

10.1093/qmath/hax031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the problem of lifting curves from finite fields to number fields in a genus and gonality preserving way. More precisely, we sketch how this can be done efficiently for curves of gonality at most four, with an in-depth treatment of curves of genus at most five over finite fields of odd characteristic, including an implementation in Magma. We then use such a lift as input to an algorithm due to the second author for computing zeta functions of curves over finite fields using p-adic cohomology.

引用

页码：33 / 74

页数：42

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