论文标题
部分可观测时空混沌系统的无模型预测
Formally regular rings and descent of regularity
论文作者
论文摘要
估值环和完美的环是（通常是非裸体）戒指的示例，在某种意义上是常规戒指。我们将常规局部环的概念扩展到非非核心环，以包括估值和完美的环，这与Grothendieck对Noetherian案件的形式平滑度的定义有关。为此，我们必须考虑拓扑。我们证明了沿扁平同构的规律定理（实际上是有限平坦维度的同态），将Notherian的一些已知结果扩展到了非Noetherian案例，并概括了非Noetherian案件中的一些最新结果，例如B. B. B. B. Bhatt，S。Iyyyengar和L. iyyyyyengar和l. iyyyyyyengar和l. iyyyyyenengar and l. iyyyyyyenengar and l. iyyyyyengar和l. iyyyyyyengar和l. iyyyyyenengar and L. iyyyyyyengar and l. iyyyyyyengar and l. iyyyyyyengar和s. iyyyyyyyengar和
Valuation rings and perfectoid rings are examples of (usually non-noetherian) rings that behave in some sense like regular rings. We give and study an extension of the concept of regular local rings to non-noetherian rings so that it includes valuation and perfectoid rings and it is related to Grothendieck's definition of formal smoothness as in the noetherian case. For that, we have to take into account the topologies. We prove a descent theorem for regularity along flat homomorphisms (in fact for homomorphisms of finite flat dimension), extending some known results from the noetherian to the non-noetherian case, as well as generalizing some recent results in the non-noetherian case, such as the descent of regularity from perfectoid rings by B. Bhatt, S. Iyengar and L. Ma.
