On the Witt vectors of perfect rings in positive characteristic

Abstract

The purpose of this article is to prove some results on the Witt vectors of perfect ${\mathbf{F}}_p$-algebras. Let $A$ be a perfect ${\mathbf{F}}_p$-algebra for a prime integer $p$ and assume that $A$ has the property $\mathbf{P}$. Then does the ring of Witt vectors of $A$ also have $\mathbf{P}$? A main theorem gives an affirmative answer for $\mathbf{P}="\mbox{integrally closed}"$ under a very mild condition.

to appear in Communications in Algebra

References in corpus (2)

• An application of the almost purity theorem to the homological conjectures
• On the Witt vector Frobenius

Cited by in corpus (3)

• A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras
• An embedding problem of Noetherian rings into the Witt vectors
• Finite étale extension of Tate rings and decompletion of perfectoid algebras