Naslov
Torsion groups of elliptic curves over quadratic fields

Autori
Najman, Filip

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

Izvornik
9th Colloquiumfest on Algebra and Logic and 8th Czech, Polish and Slovak Conference on Number Theory / - , 2010, 53-53

Skup
ALaNT – Joint Conferences on Algebra, Logic and Number Theory

Mjesto i datum
Bukowina Tatrzańska, Poljska, 21.06.2010. - 24.06.2010

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
ellipitic curves ; torsion group ; quadratic fields

Sažetak
By Mazur's torsion theorem, all the possible torsion groups of an elliptic curve over the rationals are known. By a result of Kamienny, all the possible torsion groups of an elliptic curve over all quadratic fields are also known. But Kamienny's theorem gives us no information about which torsion groups actually appear for some fixed quadratic field. We examine this problem and, for each torsion group that appears over some quadratic field, find the field with the smallest absolute value of the discriminant such that this group actually appears as torsion of an ellitpic curve. We also examine the number of elliptic curves with perscribed torsion over a fixed quadratic field.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA