Sage torsion points of jacobian

Author: mmmw

August undefined, 2024

Websage.schemes.hyperelliptic_curves.jacobian_morphism.cantor_reduction(a, b, f, h, genus)¶ Return the unique reduced divisor linearly equivalent to on the curve . See the docstring of … WebAs an application, we get a stronger result on the intersection of the theta divisor and torsion points on the Jacobian variety for more general curves. New examples are discussed as …

Quadratic torsion subgroups of modular Jacobian varieties

WebOct 22, 2012 · He then applied it to the Jacobian variety of a cyclic quotient of a Fermat curve and showed that torsion points of certain prime order lay outside of the theta … WebSep 1, 2010 · (2) As the points of a hyperelliptic curve have no structure, it is useful to examine the Jacobian variety of a curve (see [3]). Let J 1 be the Jacobian of C 1 , C (d) the quadratic twist of C 1 by d and J (d) the 1 1 Jacobian of C (d) 1 . 1966 F. Najman / Journal of NumberTheory 130 (2010) 1964–1968 Lemma 3. J 1 (Q(i)) similarequal Z 19 . Proof. for those of you watching in black and white

Introduction - University of California, Berkeley

WebGenus-2 Jacobians with torsion points of large order. Everett Howe ... WebStructure of the group of points. By the definitions, an abelian variety is a group variety. Its group of points can be proven to be commutative. For C, and hence by the Lefschetz principle for every algebraically closed field of characteristic zero, the torsion group of an abelian variety of dimension g is isomorphic to (Q/Z) 2g. WebThe difference between this point and either of the Weierstrass points is a torsion divisor of order 40, the highest known (as of 6/2001) for a simple genus-2 Jacobian. The rational … for those of you 意味

The Jacobian matrix (video) Jacobian Khan Academy

The Aluffi algebra of the Jacobian of points in projective space ...

WebAs an application, we get a stronger result on the intersection of the theta divisor and torsion points on the Jacobian variety for more general curves. ... He then applied it to the … http://fe.math.kobe-u.ac.jp/icms2010-dvd/SAGE/www.sagemath.org/doc/reference/sage/schemes/hyperelliptic_curves/jacobian_morphism.html dimension of a soda canWebNov 25, 2014 · can moreov er compute the torsion of the Aluﬃ algebra, the latter being generated by two forms in degree 2. T o understand the underlying geometric content, consider the rational map F : P 2 99K dimension of a short bond paper

"Web— The torsion point p·x ∈ Jcl K is unramiﬁed. In the present paper, we study the ramiﬁcation of torsion points on a curve such that the special ﬁber of the good model of the Jacobian variety of the curve is superspecial by means of Theorem D and some classical results in the study of ﬁnite ﬂat commutative group schemes. " - Sage torsion points of jacobian

Sage torsion points of jacobian

Genus‐2 Jacobians with torsion points of large order (English)

WebSage Days 26 December 9, 2010. Computation of p-torsion of Jacobians of ... supersingular; this distinction measures certain properties of its p-torsion. The p-torsion of the Jacobian … Weba curve that map to torsion points of the curve’s Jacobian. Let K be a number ﬁeld, and suppose that X/K is an algebraic curve1 of genus g ≥2. Assume, furthermore, that X is …

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WebJul 1, 2009 · Let us recall that zero and the six primitive λ-torsion points of J are in the Theta divisor, that all the 42 primitive λ 2-torsion points of J are outside the Theta divisor and that all the 6 × 7 2 primitive λ 3-torsion points of J are outside the Theta divisor, except for the 42 points w ± i, j, 0 (1 ≤ i ≤ 3, 0 ≤ j ≤ 6), which ... Webproperty on the point counting algorithm are also dis-cussed in this paper. In this paper, we assume that an operation of univari-ate polynomials of degree n over Fq takes O(n1+o(1)) operations in Fq. 2 Torsion points and Frobenius map Let J be the Jacobian of a genus 2 hyperelliptic curve over a ﬁnite ﬁeld Fq of odd characteristic and χ ...

WebAug 12, 2024 · The main ingredient is a method to torsion points on a Jacobian in the framework of Makdisi's algorithms to compute rho, given the characteristic polynomial of … WebJan 4, 2024 · I am interested to compute: ``torsion subgroups of Jacobian abelian variety J_0(p^2) defined over fields bigger than rationals." The command: Upto p=11 it is fine …

WebRational point sets on a Jacobian; Jacobian ‘morphism’ as a class in the Picard group; Hyperelliptic curves of genus 2 over a general ring; ... sage.schemes.elliptic_curves.ell_torsion. torsion_bound (E, number_of_places = 20) # … WebThe Jacobian of a genus-one curve can be defined as the set of line bundles on the curve, and is isomorphic to the original genus-one curve. It is also an elliptic curve with the trivial …

WebWe produce new explicit examples of genus-2 curves over the rational numbers whose Jacobian varieties have rational torsion points of large order. In particular, we produce a …

WebWe produce new explicit examples of genus‐ 2 curves over the rational numbers whose Jacobian varieties have rational torsion points of large order. In particular, we produce a … for those of you who think that gospel musicWebUsing a specialization argument, I also classify torsion points on a generic superelliptic curve, extending Theorem 7.1 of Poonen–Stoll [57] to the hyperelliptic case. In order to … for those passionate about archery codycrossWebthese points in the Jacobian [Ro]. We have proved, in particular: THEOREM B. Suppose m + 1 is prime and m 2 10. If d and e are in F(m) such that d $ e and the divisor [d -[e] is a torsion point on the Jacobian of F(m), then d and e are in c(m). These and the examples described in Section VI seem to be the only curves for those of you new to the company