论文标题
Abelian Coverings和Shimura品种的Prym品种的家族
Families of Prym varieties of abelian coverings and Shimura varieties
论文作者
论文摘要
在Prym地图具有特征性$ p $的条件下，我们证明了尺寸$ l $和极化$ D $，$ a_ {l，d，d} $的Abelian品种中的特殊次视角，是由Abelian Covers of Abelian Covers of Abelian Covers of $ Q $¶^1 $ abelian Covers of Bustrictive becultictive的本质。换句话说，如果该家庭是一维的，或者在纤维共同体中包含某些类型的特征空间，则只能由家族的小组行动来构建此类家庭的Shimura品种。
Under the condition that the Prym map is injective in characteristic $p$, we prove that the special subvarieties in the moduli space of abelian varieties of dimension $l$ and polarization type $D$, $A_{l,D}$, arising from families of abelian covers of $¶^1$ are of a very restrictive nature. In other words, if the family is one-dimensional or if it contains an eigenspace of certain type for the group action on the cohomology of fibers, then the Shimura varieties arising from such families can only be constructed by the group action of the family.
