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comment N-th root of unity in N-th division field of abelian variety?
Actually, $A^4$ does not have to be principally polarized. In fact, it does not have to be isomorphic to its dual. (As an example, you may take an abelian surface $A$ over an algebraically closed field $K$ with $\End(A)=\Z$ and such that $\Hom(A,A^t)$ is generated by the polarization $\lambda: A \to A^t$ with $\ker(\lambda)$ being a product of two cyclic groups of prime order $\ell \ne char(K)$.) It is $(A \times A^t)^4$, which is always principally polarized.
Jun
4
revised N-th root of unity in N-th division field of abelian variety?
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Jun
4
answered N-th root of unity in N-th division field of abelian variety?
May
15
comment Magnus' embedding theorem
Thank you, Igor!
May
14
comment Magnus' embedding theorem
@YCor I would appreciate a reference where such a homomorphism is explicitly described.
May
14
comment Magnus' embedding theorem
Thanks! It seems that what you denote by $F_n$ is $F/F_n$ in my notation.
May
14
asked Magnus' embedding theorem
May
9
awarded  Nice Answer
Dec
30
comment Completion of a local ring of a curve
You are welcome.
Dec
30
answered Completion of a local ring of a curve
Nov
25
comment Fermat's last theorem over larger fields
The reference above contains an abstract in English. However, the paper is available in English as well: mr.crossref.org/iPage?doi=10.1070%2FIM2001v065n03ABEH000337 .
Nov
25
answered Fermat's last theorem over larger fields
Sep
30
awarded  Yearling
Sep
19
answered Endomorphism Ring of Simple Abelian Varieties
Jun
4
awarded  Enlightened
Jun
4
awarded  Nice Answer
May
15
awarded  Good Answer
Jan
14
awarded  Nice Answer
Dec
13
awarded  ag.algebraic-geometry
Dec
12
comment Mumford-Tate groups of products of Hodge structures
Yes, you are right: please see my counterexample below.