Zusammenfassung
Let A be an abelian variety defined over a number field K. Let p be a prime of K of good reduction and A(p) the fiber of A over the residue field k(p). We call A(K)(p) the image of the Mordell-Weil group via reduction modulo p, which is a subgroup of A(p)(k)(p). We prove in particular that the size of A(K)(p), by varying p, encodes enough information to characterize the K-isogeny class of A, ...
Zusammenfassung
Let A be an abelian variety defined over a number field K. Let p be a prime of K of good reduction and A(p) the fiber of A over the residue field k(p). We call A(K)(p) the image of the Mordell-Weil group via reduction modulo p, which is a subgroup of A(p)(k)(p). We prove in particular that the size of A(K)(p), by varying p, encodes enough information to characterize the K-isogeny class of A, provided that the following necessary condition holds: the Mordell-Weil group A(K) is Zariski dense in A. This is an analogue a 1983 result of Faltings, considering instead the size of A(p)(k(p)).
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