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From the answer of the above question, we know T. Shioda in "Some remarks on Abelian varieties" found counter-examples of the "cancellation law" of abelian varieties. From the mathscinet review I found that in particular Shioda found elliptic curves $E$, $E^{\prime}$ and $E^{\prime\prime}$ such that $E\times E^{\prime\prime}$ is isomorphic to $E^{\prime}\times E^{\prime\prime}$ but $E$ is not isomorphic to $E^{\prime}$.

I don't have the access to the above paper. Is there anyone who has some ideas on how do construct this example?


1 Answer 1


Here is the paper you seek, by Tetsuji Shioda, on "Some remarks on Abelian varieties." Hope the counter-examples there help you.


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