• Corpus ID: 248119125

Torsion phenomena for zero-cycles on a product of curves over a number field

@inproceedings{Gazaki2022TorsionPF,
  title={Torsion phenomena for zero-cycles on a product of curves over a number field},
  author={Evangelia Gazaki and Jonathan Love},
  year={2022}
}
. For a smooth projective variety X over a number field k a conjecture of Bloch and Beilinson predicts that the kernel of the Albanese map of X is a torsion group. In this article we consider a product X = C 1 ×· · ·× C d of smooth projective curves and show that if the conjecture is true for any subproduct of two curves, then it is true for X . Additionally, we produce many new examples of non-isogenous elliptic curves E 1 , E 2 with positive rank over Q for which the image of the natural map E… 

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SHOWING 1-10 OF 22 REFERENCES
Weak Approximation for $0$-cycles on a product of elliptic curves
In the 1980’s Colliot-Thélène, Sansuc, Kato and S. Saito proposed conjectures related to local-to-global principles for 0-cycles on arbitrary smooth projective varieties over a number field. We give
Rational Equivalences on Products of Elliptic Curves in a Family
  • Jonathan Love
  • Mathematics, Computer Science
    Journal de Théorie des Nombres de Bordeaux
  • 2021
TLDR
A $2-parameter family of elliptic curves that can be used to produce examples of pairs where this image of this map is finite when $k$ is a number field is constructed.
Nullité de certains groupes attachés aux variétés semi-abéliennes sur un corps fini; application
Soient G 1 ,...,G n des varietes semi-abeliennes sur un corps fini F. On montre que, si n≥2, K(F,G 1 ,...,G n )=0 ou K(F,G 1 ,...,G n ) est le groupe defini dans [1] par Somekawa. On utilise ce
Algebraic Groups and Class Fields
Summary of the main results algebraic curves maps from a curve to a commutative group singular algebraic curves generalized jacobians class field theory group extension and cohomology.
Algebraic cycles and values of L-functions.
Let X be a smooth projective algebraic variety of dimension d over a number field k, and let n ̂ 0 be an integer, /-adic cohomology in degree /i, H(X^, Ot), is a representation space for Gal (Jc/k)
Milnor K-Groups and Zero-Cycles on Products of Curves over p-Adic Fields
We investigate the Chow groups of zero cycles of products of curves over a p-adic field by means of the Milnor K-groups of their Jacobians as introduced by Somekawa. We prove some finiteness results
Genus 2 curves with given split Jacobian
  • J. Scholten
  • Mathematics, Computer Science
    IACR Cryptol. ePrint Arch.
  • 2018
TLDR
Given 2 Elliptic Curves E1 and E2, some theory of elliptic Kummer surfaces is used to construct a hyperelliptic curve with Jacobian isogenous to E1 × E2 with 2-torsion defined over the field the authors are working over.
...
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