engleski

Growth of torsion groups of elliptic curves upon base change

We study how the torsion of elliptic curves over number fields grows upon base change, and in particular prove various necessary conditions for torsion growth. For a number field F, we show that for a large set of number fields L, whose Galois group of their normal closure over F has certain properties, it will hold that E(L)tors = E(F)tors for all elliptic curves E defined over F.

elliptic curves ; torsion over number fields

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