Abelian Subvarieties
نویسندگان
چکیده
منابع مشابه
Subvarieties of Abelian Varieties
Let (A; ) be a principally polarized abelian variety (ppav) of dimension g over the eld C of complex numbers. This means that is an ample divisor on A, well-determined up to translation, with h(A; ) := dimH(A; ) = 1. Let [ ] 2 H(A;Z) be the cohomology class of the theta divisor . Then the cohomology class [ ] e is divisible by (g e)!. The class [ ] g e (g e)! is not divisible and it is called t...
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Let (W, ω) be a smooth projective algebraic variety of dimension 2n over C together with a holomorphic (2, 0)-form of maximal rank 2n. A subvariety X ⊂ W is called weakly lagrangian if dim X ≤ n and if the restriction of ω to X is trivial (notice that X can be singular). An n-dimensional subvariety X ⊂ W with this property is called lagrangian. For example, any curve C contained in a K3 or abel...
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The purpose of this note is to show that the Shimura construction follows from a general “dictionary” that translates statements about subvarieties of abelian varieties into statements about ideals of the associated endomorphism algebras. Theorem. Let A/K be an abelian variety with endomorphism algebra E = End0K(A). Then the map B 7→ I(B) := {f ∈ E : Imf ⊂ B} defines an inclusion-preserving bij...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1996
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0079