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Jacobian Varieties of Hyperelliptic Curves with Mixed Symmetric Formal Type
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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 en- domorphism of the Jacobian variety. It gives a useful tool for finding the local decomposition of the Jacobian variety into isotypic components.
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 en- domorphism of the Jacobian variety. It gives a useful tool for finding the local decomposition of the Jacobian variety into isotypic components.
참고문헌 (7)
- Yu. I. Manin, "The Hasse-Witt matrix of an algebraic curve", AMS Trans. Ser. 2, (45), pp.245~264 (1965)
- F. Oort, "Arithmetic algebraic geometry", pp.247~284 (1991), birkhäuser Boston
- R. Pries, "The p-torsion of curves with large p-rank", Int. J. Number Theory, 5(6), pp.1103~1116 (2009)
- J. Scholten, "Hyperelliptic curves in characteristic 2", Int. Math. Res. Not, (17), pp.905~917 (2002)
- N. Yui, "On the Jacobian varieties of hyperelliptic curves over fields of characteristic p > 2", J. Algebra, 52(2), pp.378~410 (1978)
- A. Weil, "Sur les courbes algébriques et les variétés qui s’en déduisent" (1948), Hermann et Cie
- A. Weil, "Variétés abéliennes et courbes algébriques" (1948), Her-mann & Cie
관련 논문AI추천
Jacobian Varieties of Hyperelliptic Curves over Finite Fields with the Formal Structure of the Mixed Type손교용영남수학회 · East Asian Mathematical Journal2021 · 제37권 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 제2호Isomorphism classes of genus-3 pointed trigonal curves over finite fields of characteristic 2강병련, 선선미대한수학회 · 대한수학회보2009 · 제46권 제5호Weierstrass points on hyperelliptic modular curves전대열대한수학회 · 대한수학회논문집2015 · 제30권 제4호THE BOUNDS OF THE COEFFICIENTS OF THE CHARACTERISTIC POLYNOMIALS FOR ABELIAN VARIETIES OF DIMENSION 5 OVER FINITE FIELDS손교용장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제3호
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