CM Jacobians
نویسنده
چکیده
1. Complex multiplication. We say an abelian variety A of dimension g over a field K admits sufficiently many Complex Multiplications (smCM) if D = End(A) contains a commutative semi-simple algebra Λ ⊂ D of rank dimQ(Λ) = [Λ : Q] = 2g. In this case we say A is a CM abelian variety. A point z ∈ Ag(k) is called a CM point if z is the moduli point of a polarized abelian variety z = [(A,μ)] such that A is a CM abelian variety. If an algebraic curve C has a Jacobian J(C) which is a CM abelian variety we say C is a CM curve.
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