论文标题
通过分层的方案和完美的空间上的圆锥积分
Conical calculus on schemes and perfectoid spaces via stratification
论文作者
论文摘要
在本文中，我们表明，除了涉及kähler差异的常规演算外，还可以在方案和完美的空间上定义锥形积分。这可以通过分层过程来完成。按照[1-2]的一些想法，我们考虑了这些空间的一些自然分层，然后我们基于Ayala，Francis和Tanaka [3]的工作（另见[4-5]和[18]）；利用它们对分层空间的衍生物，平滑度和向量场的定义，并且由于某些特定的方法，我们能够将这些概念传输到方案和完美的空间。这也使我们能够定义锥形差分形式和圆锥形DE RHAM复合物。最后，我们将此方法与通常的方法进行了比较，并指出它是Kähler方法的有用\ textit {添加}。
In this paper we show that, besides the usual calculus involving Kähler differentials, it is also possible to define conical calculus on schemes and perfectoid spaces; this can be done via a stratification process. Following some ideas from [1-2], we consider some natural stratifications of these spaces and then we build upon the work of Ayala, Francis, and Tanaka [3] (see also [4-5] and [18]); using their definitions of derivatives, smoothness and vector fields for stratified spaces, and thanks to some particular methods, we are able to transport these concepts to schemes and perfectoid spaces. This also allows us to define conical differential forms and the conical de Rham complex. At the end, we compare this approach with the usual one, noting that it is a useful \textit{addition} to Kähler method.
