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Jacobian Varieties of Hyperelliptic Curves over Finite Fields with the Formal Structure of the Mixed Type

손교용
영남수학회 (Youngnam Mathematical Society)|2021.09|East Asian Mathematical Journal|제37권 제5호|pp. 585-590

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참고문헌

키워드

Jacobian varietyHyperelliptic Curve
주제분류수학

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.

Abstract

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.

참고문헌 (7)

  1. Yu. I. Manin, "The Hasse-Witt matrix of an algebraic curve", AMS Trans. Ser. 2, 45, pp.245~264 (1965)
  2. F. Oort, "Hyperelliptic supersingular curves, Arithmetic algebraic geometry (Texel, 1989)", Progr. math, 89, pp.247~284 (1989)
  3. R. Pries, "The p-torsion of curves with large p-rank", Int. J. Number Theory, 5(6), pp.1103~1116 (2009)
  4. J. Scholten, "Hyperelliptic curves in characteristic 2", Int. Math. Res. Not, 17, pp.905~917 (2002)
  5. N. Yui, "On the Jacobian Varieties of Hyperelliptic Curves over Fields of Characteristic p > 2", Journal of Algebra, 52(2), pp.378~410 (1978)
  6. A. Weil, "Sur les courbes algebriques et les varietes qui s'en deduisent", Actualites Sci. Ind, (1041) (1948), Hermann et Cie
  7. A. Weil, "Varietes abeliennes et courbes algebriques", Actualites Sci. Ind, (1064) (1948), Hermann & Cie

관련 논문AI추천

Jacobian Varieties of Hyperelliptic Curves with Mixed Symmetric Formal Type손교용영남수학회 · East Asian Mathematical Journal2022 · 제38권 제5호STUDY ON THE JACOBIAN VARIETIES OF HYPERELLIPTIC CURVES OVER FINITE FIELDS손교용장전수학회 · Advanced Studies in Contemporary Mathematics2020 · 제30권 제3호Average values on the Jacobian variety of a hyperelliptic curve임보해, 정지만대한수학회 · 대한수학회보2019 · 제56권 제2호THE BOUNDS OF THE COEFFICIENTS OF THE CHARACTERISTIC POLYNOMIALS FOR ABELIAN VARIETIES OF DIMENSION 5 OVER FINITE FIELDS손교용장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제3호Isomorphism classes of genus-3 pointed trigonal curves over finite fields of characteristic 2강병련, 선선미대한수학회 · 대한수학회보2009 · 제46권 제5호The Newton polygons of the characteristic polynomials for Abelian varieties of dimension 5 over finite fields손교용장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제4호

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