Tracking issue: The Tilting Equivalence of Perfectoid Fields

[jjdishere]

This issue is meant to track PRs on the development of the theory of perfectoid fields. This issue belongs to a broader project of proving the Fontaine-Wintenberger theorem.

Rough roadmap:

• define the topological nilpotent elements and bounded elements
• define the pefectoid fields
• show that the tilt of a perfectoid field is still perfectoid (to be decomposed later)
• define the tilt of the morphism
• define the category of perfectoid fields and the tilting functor
• show that char p perfectoid field is just a rank 1 valued perfect char p field

Open or already closed PRs on this topic: