论文标题
具有复杂乘法的椭圆形曲线的偏光产品和模量$ \ mathbb {q} $的字段
Polarized products of elliptic curves with complex multiplication and field of moduli $\mathbb{Q}$
论文作者
论文摘要
令$ r $为二次假想字段$ k $中的最大订单。我们将偏光化的Abelian品种类别同构的类别等效到与$ \ Mathbb {CM）的椭圆形曲线的产物，并通过$ r $与$ r $的复杂乘法（cm）和整体Hermitian $ r $ r $ lub-lastices的类别。然后，我们将这种等价列举以使用Moduli $ \ Mathbb {Q} $的字段列举所有属$ 2 $和$ 3 $曲线，并与Jacobian同构为CM By $ R $的椭圆曲线的产品。
Let $R$ be the maximal order in a quadratic imaginary field $K$. We give an equivalence of categories between the category of polarized abelian varieties isomorphic to a product of elliptic curves over $\mathbb{C}$ with complex multiplication (CM) by $R$ and the category of integral hermitian $R$-lattices. Then we apply this equivalence to enumerate all the genus $2$ and $3$ curves with field of moduli $\mathbb{Q}$ and with Jacobian isomorphic to a product of elliptic curves with CM by $R$.
