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JACOBIAN VARIETIES OF HYPERELLIPTIC CURVES OVER FINITE FIELDS WITH THE FORMAL STRUCTURE OF THE MIXED TYPE

  • Sohn, Gyoyong (Department of Mathematics Educaiton, Daegu National University of Education)
  • 투고 : 2021.07.15
  • 심사 : 2021.09.27
  • 발행 : 2021.09.30

초록

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

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참고문헌

  1. Yu. I. Manin, The Hasse-Witt matrix of an algebraic curve, AMS Trans. Ser. 2, 45 (1965), 245-264.
  2. F. Oort, Hyperelliptic supersingular curves, Arithmetic algebraic geometry (Texel, 1989), Progr. math.,89, birkhauser Boston, Boston, MA, (1991), 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, Journal of 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.