Naslov
A criterion for injectivity of the specialization homomorphism of elliptic curves and its applications

Autori
Tadić, Petra

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Computational Aspects of Diophantine Equations / - , 2016, 26-26

Skup
Computational Aspects of Diophantine Equations

Mjesto i datum
Salzburg, Austrija, 15.02.2016. - 19.02.2016

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
elliptic curves ; rank ; function fields ; generators ; injectivity ; specialization homomorphism

Sažetak
Let $K$ be a number field. Let $E$ be a nonconstant elliptic curve over $K(t)$ with at least one nontrivial $K(t)$-rational $2$- torsion point. By the Silverman specialization theorem the specialization homomorphism $t\mapsto t_0$ is injective for all but finitely many $t_0\in K$. For $K$ of class number one, Gusi\' c and Tadi\' c obtained a method for finding $t_0\in K$ for which the corresponding specialization homomorphism is injective. In principal they extended the method to arbitrary number fields $K$. This method can be used to calculate the rank of elliptic curves of the form as above, by looking at the structure of a chosen specialized curve. This method has been used by Gusi\' c, Dujella, Peral and Tadi\' c to calculate exactly the rank of some record high rank elliptic curves over $\mathbb Q(t).$

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA