[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7858/eamj.2022.037

JACOBIAN VARIETIES OF HYPERELLIPTIC CURVES WITH MIXED SYMMETRIC FORMAL TYPE

Sohn, Gyoyong (Department of Mathematics Education, Daegu National University of Education)

Publication Information

East Asian mathematical journal / v.38, no.5, 2022 , pp. 611-616 More about this Journal

Abstract

This paper considers the Jacobian variety of a hyperelliptic curve over a finite field with mixed symmetric formal type. We present the Newton polygon of the characteristic polynomial of the Frobenius endomorphism of the Jacobian variety. It gives a useful tool for finding the local decomposition of the Jacobian variety into isotypic components.

Keywords

Hyperellitpic curves over finite fields;

Citations & Related Records

Reference

1	Yu. I. Manin, The Hasse-Witt matrix of an algebraic curve, AMS Trans. Ser. 2. (1965), no. 45, 245-264.
2	R. Pries, The p-torsion of curves with large p-rank, Int. J. Number Theory. 5 (2009), no. 6, 1103-1116. DOI
3	A. Weil, Sur les courbes algebriques et les varietes qui s'en deduisent, Actualites Sci. Ind., no. 1041, Hermann et Cie.. Paris, 1948.
4	F. Oort, Hyperelliptic supersingular curves, Arithmetic algebraic geometry (Texel, 1989), Progr. math., vol. 89, birkhauser Boston, Boston, MA, 1991, pp. 247-284.
5	J. Scholten and H. J. Zhu, Hyperelliptic curves in characteristic 2, Int. Math. Res. Not. (2002), no. 17, 905-917.
6	N. Yui, On the Jacobian varieties of hyperelliptic curves over fields of characteristic p > 2, J. Algebra. 52 (1978), no. 2, 378-410. DOI
7	A. Weil, Varietes abeliennes et courbes algebriques, Actualites Sci. Ind., no. 1064, Hermann & Cie., Paris, 1948.