The existence of supersingular curves of genus 4 in arbitrary characteristic

被引：5

作者：

Kudo, Momonari ^{[1
]}

Harashita, Shushi ^{[2
]}

Senda, Hayato ^{[2
]}

机构：

[1] Univ Tokyo, Grad Sch Informat Sci & Technol, Dept Math Informat, Tokyo, Japan

[2] Yokohama Natl Univ, Grad Sch Environm & Informat Sci, Yokohama, Kanagawa, Japan

来源：

RESEARCH IN NUMBER THEORY | 2020年 / 6卷 / 04期

关键词：

HYPERELLIPTIC CURVES;

D O I：

10.1007/s40993-020-00217-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that there exists a supersingular nonsingular curve of genus 4 in arbitrary characteristic p > 0. For p > 3 we shall prove that the desingularization of a certain fiber product over P-1 of two supersingular elliptic curves is supersingular.

引用

页数：17

共 23 条

[1]

Achter J, 2019, ARITHMETIC GEOMETRY, V722

[2] Monodromy and irreducibility of leaves [J].

Chai, Ching-Li ;

Oort, Frans .

ANNALS OF MATHEMATICS, 2011, 173 (03) :1359-1396

[3] Purity of the stratification by Newton polygons [J].

De Jong, AJ ;

Oort, F .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 13 (01) :209-241

[4]

Deuring M., 1941, ABH MATH SEM HAMBURG, V14, P197

[5] Hyperelliptic curves with prescribed p-torsion [J].

Glass, D ;

Pries, R .

MANUSCRIPTA MATHEMATICA, 2005, 117 (03) :299-317

[6] Hasse-Witt matrices for the Fermat curves of prime degree [J].

Gonzalez, J .

TOHOKU MATHEMATICAL JOURNAL, 1997, 49 (02) :149-163

[7] Ekedahl-Oort strata and the first Newton slope strata [J].

Harashita, Shushi .

JOURNAL OF ALGEBRAIC GEOMETRY, 2007, 16 (01) :171-199

[8]

Hartshorne Robin, 1977, Graduate Texts in Mathematics, V52

[9] Quickly constructing curves of genus 4 with many points [J].

Howe, Everett W. .

FROBENIUS DISTRIBUTIONS: LANG-TROTTER AND SATO-TATE CONJECTURES, 2016, 663 :149-173

[10] ON RATIONAL-POINTS OF CURVES OF GENUS-3 OVER FINITE-FIELDS [J].

IBUKIYAMA, T .

TOHOKU MATHEMATICAL JOURNAL, 1993, 45 (03) :311-329

← 1 2 3 →