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- W3102052893 abstract "Let $A$ be an abelian variety defined over a number field $K$. If $mathfrak{p}$ is a prime of $K$ of good reduction for $A$, let $A(K)_mathfrak{p}$ denote the image of the Mordell-Weil group via reduction modulo $mathfrak{p}$. We prove in particular that the size of $A(K)_mathfrak{p}$, by varying $mathfrak{p}$, encodes enough information to determine the $K$-isogeny class of $A$, provided that the following necessary condition is satisfied: $B(K)$ has positive rank for every non-trivial abelian subvariety $B$ of $A$. This is the analogue to a result by Faltings of 1983 considering instead the Hasse-Weil zeta function of the special fibers $A_mathfrak{p}$." @default.
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- W3102052893 date "2013-08-28" @default.
- W3102052893 modified "2023-09-27" @default.
- W3102052893 title "Characterizing abelian varieties by the reduction of the Mordell–Weil group" @default.
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- W3102052893 doi "https://doi.org/10.2140/pjm.2013.265.427" @default.
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