Maps between curves and arithmetic obstructions

被引：4

作者：

Sutherland, Andrew V. ^{[1
]}

Voloch, Jose Felipe ^{[2
]}

机构：

[1] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] Univ Canterbury, Sch Math & Stat, Private Bag 4800, Christchurch 8140, New Zealand

来源：

ARITHMETIC GEOMETRY: COMPUTATION AND APPLICATIONS | 2019年 / 722卷

基金：

美国国家科学基金会;

关键词：

HASSE-WITT MATRICES; HYPERELLIPTIC CURVES; FUNCTION-FIELDS;

D O I：

10.1090/conm/722/14532

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X and Y be curves over a finite field. In this article we explore methods to determine whether there is a rational map from Y to X by considering L-functions of certain covers of X and Y and propose a specific family of covers to address the special case of determining when X and Y are isomorphic. We also discuss an application to factoring polynomials over finite fields.

引用

页码：167 / 175

页数：9

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