论文标题
部分可观测时空混沌系统的无模型预测
Abelian Varieties with $p$-rank Zero
论文作者
论文摘要
有一个众所周知的定理，该定理给出了一个标准，即当通过假想二次场的整数中的复杂乘法（CM）还原椭圆形曲线时，具有普通的或超单向的还原。我们将其概括为Goren在Dimension 2中的类似定理，并对$ p $ torsion组方案进行分类，以减少3二维Abelian品种，用CM通过CM的环形环，环状六频CM领域的整数环。我们还证明了一个定理的任意维度$ g $，可以通过CM的循环CM $ 2G $ $ 2G $区分普通和超级缩短的Abelian品种。作为一种应用，我们给出了算法来构建尺寸2（表面）和尺寸3的超级非苏格，以及超级专门的阿伯利亚品种，并证明所有这些品种都具有小度的非直觉内态性。
There is a well known theorem by Deuring which gives a criterion for when the reduction of an elliptic curve with complex multiplication (CM) by the ring of integers of an imaginary quadratic field has ordinary or supersingular reduction. We generalise this and a similar theorem by Goren in dimension 2, and classify the $p$-torsion group scheme of the reduction of 3-dimensional abelian varieties with CM by the ring of integers of a cyclic sextic CM field. We also prove a theorem in arbitrary dimension $g$ that distinguishes ordinary and superspecial reduction for abelian varieties with CM by a cyclic CM field of degree $2g$. As an application, we give algorithms to construct supersingular non-superspecial, and superspecial abelian varieties of dimension 2 (surfaces) and dimension 3, and show that all such varieties have non-integer endomorphisms of small degree.
