منابع مشابه
Weierstrass semigroups from Kummer extensions
The Weierstrass semigroups and pure gaps can be helpful in constructing codes with better parameters. In this paper, we investigate explicitly the minimal generating set of the Weierstrass semigroups associated with several totally ramified places over arbitrary Kummer extensions. Applying the techniques provided by Matthews in her previous work, we extend the results of specific Kummer extensi...
متن کاملm at h . A G ] 1 9 Fe b 20 14 Weierstrass points on Kummer extensions
Let F be an algebraic function field in one variable defined over an algebraically closed field K of characteristic p ≥ 0. For any given place P of F , a number s is called a non-gap at P if there exists a function z ∈ F such that the pole divisor of z is (z)∞ = sP . If there is no such function, the number s is called a gap at P . If g is the genus of F , it follows from the Riemann-Roch theor...
متن کاملHeegner Points over Towers of Kummer Extensions
Let E be an elliptic curve, and let Ln be the Kummer extension generated by a primitive pnth root of unity and a pn-th root of a for a fixed a ∈ Q − {±1}. A detailed case study by Coates, Fukaya, Kato and Sujatha and V. Dokchitser has led these authors to predict unbounded and strikingly regular growth for the rank of E over Ln in certain cases. The aim of this note is to explain how some of th...
متن کاملOn Weierstrass Points and Optimal Curves
We use Weierstrass Point Theory and Frobenius orders to prove the uniqueness (up to isomorphism) of some optimal curves. This paper continues the study, begun in [FT] and [FGT], of curves over finite fields with many rational points, based on Stöhr-Voloch’s approach [SV] to the Hasse-Weil bound by way of Weierstrass Point Theory and Frobenius orders. Some of the results were announced in [T]. A...
متن کاملOn the Constellations of Weierstrass Points
We prove that the constellation of Weierstrass points characterizes the isomorphism-class of double coverings of curves of genus large enough. 1. Let X be a projective, irreducible, non-singular algebraic curve defined over an algebraically closed field k of characteristic p. Let n ≥ 1 be an integer and CX a canonical divisor of X. The pluricanonical linear system |nCX | defines a nondegenerate...
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ژورنال
عنوان ژورنال: Advances in Geometry
سال: 2018
ISSN: 1615-7168,1615-715X
DOI: 10.1515/advgeom-2018-0021