基于分层的概型和拟完全空间上的锥演算
Conical calculus on schemes and perfectoid spaces via stratification
摘要：
在本文中，我们表明，除了通常的微积分涉及凯勒微分，它也可以定义锥演算计划和perfectoid空间，这可以通过分层过程。根据[1-2]中的一些思想，我们考虑这些空间的一些自然分层，然后我们建立在Ayala，Francis和Tanaka [3]的工作基础上（参见[4-5]和[18]）;使用他们对分层空间的导数，光滑性和向量场的定义，并且由于一些特殊的方法，我们能够将这些概念转移到概型和完美空间。这也允许我们定义圆锥微分形式和圆锥德拉姆复形。最后，我们将这种方法与通常的方法进行了比较，指出它是一种有用的\textit{addition}到Kähler方法。
英文摘要：
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.
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