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added some minimum content to perfectoid space. Also added a corresponding paragraph to function field analogy.
Since my chapter in What is a mathematical concept? appears next to Michael Harris’s ’The perfectoid concept: test case for an absent theory’, when I get a chance to read that it would fun to see what sense I can make of the idea.
A throw-away thought: if, as Scholze says, perectoids were devised to mediate between $\mathbb{Q}_p$ and $\mathbb{F}_p((t))$, and
Although these two fields have formally ’the same’ elements, the basic addition and multiplication operations are different: In $\mathbb{Q}_p$, one computes with carry, but in $\mathbb{F}_p((t))$ without carry,
is it interesting that carrying is a form of cohomology?
Michael Harris: The Perfectoid Concept: Test Case for an Absent Theory (pdf, 12pp)
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