论文标题
部分可观测时空混沌系统的无模型预测
Differentiably simple rings and ring extensions defined by $p$-basis
论文作者
论文摘要
我们回顾了不同简单戒指的概念，并给出了Harper定理的新证明，内容涉及Noetherian的表征，以积极的特征分化。然后，我们研究了不同的简单环的平坦家族，或同等的，有限的平坦延伸仪，这些环在本地接纳$ p $ basis。这些扩展名为“指数的Galois扩展名”。对于这样的扩展$ A \子集C $，我们引入了$ a $ -scheme，称为“ yuan scheme”，该计划将subextensions $ a \ subset b \ subset c $参数化，以使$ b \ subset c $是固定等级的galois。因此，大概，可以将元的计划视为Galois范围的一种司法。我们最终证明了元方案是平滑的，并计算纤维的尺寸。
We review the concept of differentiably simple ring and we give a new proof of Harper's Theorem on the characterization of Noetherian differentiably simple rings in positive characteristic. We then study flat families of differentiably simple rings, or equivalently, finite flat extensions of rings which locally admit $p$-basis. These extensions are called "Galois extensions of exponent one". For such an extension $A\subset C$, we introduce an $A$-scheme, called the "Yuan scheme", which parametrizes subextensions $A\subset B\subset C$ such that $B\subset C$ is Galois of a fixed rank. So, roughly, the Yuan scheme can be thought of as a kind of Grassmannian of Galois subextensions. We finally prove that the Yuan scheme is smooth and compute the dimension of the fibers.
