Tilting Correspondences of Perfectoid Rings
arXiv:2110.10120
Abstract
In this article, we present an alternate proof of a vanishing result of étale cohomology on perfectoid rings due to Česnavičius and more recently proved by a different approach by Bhatt and Scholze. To establish that, we prove a tilting equivalence of étale cohomology of perfectoid rings taking values in commutative, finite étale group schemes. On the way, we algebraically establish an analogue of the tilting correspondences of Scholze, between the category of finite étale schemes over a perfectoid ring and that over its tilt, without using tools from almost ring theory or adic spaces.
12 pages, comments welcome!