Naslov
Injectivity of the specialization homomorphism of elliptic curves

Autori
Tadić, Petra

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

Izvornik
Workshop on Number Theory and Algebra / - , 2014, 13-13

Skup
Workshop on Number Theory and Algebra on the occasion of 60th birthday of Ivica Gusić

Mjesto i datum
Zagreb, Hrvatska, 26.11.2014. - 28.11.2014

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
elliptic curve; specialization homomorphism

Sažetak
Let E be a nonconstant elliptic curve over Q(t) with at least one nontrivial Q(t)-rational 2-torsion point. By the Silverman specialization theorem the specialization homomorphism t --> t0 is injective for all but finitely many t0 ∈ Q. We describe a method for finding t0 ∈ Q for which the corresponding specialization homomorphism is injective. The method can be directly extended to elliptic curves over K(t) for a number field K of class number 1, and in principal for arbitrary number field K. This is an improvement of a result from one of our former preprints on this topic. We show how this method can be used to calculate the rank of elliptic curves over Q(t) of the form as above, by observing a chosen specialized curve. This is a joint work with I. Gusic.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA