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

共 17 条

[1]

Barkley Rosser J., 1962, Illinois J. Math., V6, P64

[2]

Bosma W., 2017, HDB MAGMA FUNCTIONS

[3]

BUIUM A, 1993, ASTERISQUE, P35

[4] Real polynomials with all roots on the unit circle and abelian varieties over finite fields [J].

DiPippo, SA ;

Howe, EW .

JOURNAL OF NUMBER THEORY, 1998, 73 (02) :426-450

[5] Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time, II [J].

Harvey, David ;

Sutherland, Andrew V. .

FROBENIUS DISTRIBUTIONS: LANG-TROTTER AND SATO-TATE CONJECTURES, 2016, 663 :127-147

[6] Computing zeta functions of arithmetic schemes [J].

Harvey, David .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2015, 111 :1379-1401

[7] Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time [J].

Harvey, David ;

Sutherland, Andrew V. .

LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2014, 17 :257-273

[8]

Hess F, 2004, LECT NOTES COMPUT SC, V3076, P263

[9] Constructing distinct curves with isomorphic Jacobians [J].

Howe, EW .

JOURNAL OF NUMBER THEORY, 1996, 56 (02) :381-390

[10]

Kedlaya KS, 2008, LECT NOTES COMPUT SC, V5011, P312, DOI 10.1007/978-3-540-79456-1_21

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