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Akademický článek
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Autor:
YAN, Jiali
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2023 Jan 01. 35(3), 659-674.
Externí odkaz:
https://www.jstor.org/stable/48766115
Autor:
Fisher, Tom, Yan, Jiali
We describe a method for computing the Cassels-Tate pairing on the 2-Selmer group of the Jacobian of a genus 2 curve. This can be used to improve the upper bound coming from 2-descent for the rank of the group of rational points on the Jacobian. Our
Externí odkaz:
http://arxiv.org/abs/2306.06011
Autor:
Shukla, Himanshu, Stoll, Michael
We explicitly compute the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve using the Albanese-Albanese definition of the pairing given by Poonen and Stoll. This leads to a new proof that a pairing defined by Cassels on the 2-Selmer gro
Externí odkaz:
http://arxiv.org/abs/2302.01640
Autor:
Fisher, Tom
We use the invariant theory of binary quartics to give a new formula for the Cassels-Tate pairing on the $2$-Selmer group of an elliptic curve. Unlike earlier methods, our formula does not require us to solve any conics. An important role in our cons
Externí odkaz:
http://arxiv.org/abs/2208.14977
Autor:
Morgan, Adam, Smith, Alexander
In previous work, the authors defined a category $SMod_F$ of finite Galois modules decorated with local conditions for each global field $F$. In this paper, given an extension $K/F$ of global fields, we define a restriction of scalars functor from $S
Externí odkaz:
http://arxiv.org/abs/2206.13403
Autor:
Yan, Jiali
In this paper, we give an explicit formula as well as a practical algorithm for computing the Cassels-Tate pairing on $\text{Sel}^{2}(J) \times \text{Sel}^{2}(J)$ where $J$ is the Jacobian variety of a genus two curve under the assumption that all po
Externí odkaz:
http://arxiv.org/abs/2109.08258
Autor:
Yan, Jiali
In this paper, we study the Cassels-Tate pairing on Jacobians of genus two curves admitting a special type of isogenies called Richelot isogenies. Let $\phi: J \rightarrow \widehat{J}$ be a Richelot isogeny between two Jacobians of genus two curves.
Externí odkaz:
http://arxiv.org/abs/2109.08257
Autor:
Morgan, Adam, Smith, Alexander
Given a global field $F$ with absolute Galois group $G_F$, we define a category $SMod_F$ whose objects are finite $G_F$-modules decorated with local conditions. We define this category so that `taking the Selmer group' defines a functor $Sel$ from $S
Externí odkaz:
http://arxiv.org/abs/2103.08530
Akademický článek
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