DOI QR코드

DOI QR Code

JACOBIAN VARIETIES OF HYPERELLIPTIC CURVES WITH MIXED SYMMETRIC FORMAL TYPE

  • Sohn, Gyoyong (Department of Mathematics Education, Daegu National University of Education)
  • Received : 2022.04.29
  • Accepted : 2022.09.15
  • Published : 2022.09.30

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

References

  1. Yu. I. Manin, The Hasse-Witt matrix of an algebraic curve, AMS Trans. Ser. 2. (1965), no. 45, 245-264.
  2. F. Oort, Hyperelliptic supersingular curves, Arithmetic algebraic geometry (Texel, 1989), Progr. math., vol. 89, birkhauser Boston, Boston, MA, 1991, pp. 247-284.
  3. R. Pries, The p-torsion of curves with large p-rank, Int. J. Number Theory. 5 (2009), no. 6, 1103-1116. https://doi.org/10.1142/S1793042109002560
  4. J. Scholten and H. J. Zhu, Hyperelliptic curves in characteristic 2, Int. Math. Res. Not. (2002), no. 17, 905-917.
  5. N. Yui, On the Jacobian varieties of hyperelliptic curves over fields of characteristic p > 2, J. Algebra. 52 (1978), no. 2, 378-410. https://doi.org/10.1016/0021-8693(78)90247-8
  6. A. Weil, Sur les courbes algebriques et les varietes qui s'en deduisent, Actualites Sci. Ind., no. 1041, Hermann et Cie.. Paris, 1948.
  7. A. Weil, Varietes abeliennes et courbes algebriques, Actualites Sci. Ind., no. 1064, Hermann & Cie., Paris, 1948.