isomorphism of abelian varieties - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T06:39:34Z http://mathoverflow.net/feeds/question/20791 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/20791/isomorphism-of-abelian-varieties isomorphism of abelian varieties Tuan 2010-04-08T21:56:00Z 2010-04-09T03:44:09Z <p>Let $A, B, C$ and $D$ be abelian varieties (over $\mathbb{C}$) such that $A \times B \cong C \times D$, and $A \cong C$. From the irreducibility of abelian varieties, we can say that $B$ and $D$ are isogeneous. But do we actually have $B \cong D$?</p> http://mathoverflow.net/questions/20791/isomorphism-of-abelian-varieties/20811#20811 Answer by Angelo for isomorphism of abelian varieties Angelo 2010-04-09T03:44:09Z 2010-04-09T03:44:09Z <p>This is false even for elliptic curves over $\mathbb{C}$. This was proved by T. Shioda in "Some remarks on abelian varieties" J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977), no. 1, 11-21, <a href="http://repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/6164/1/jfs240102.pdf" rel="nofollow">http://repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/6164/1/jfs240102.pdf</a>.</p>