Journal of the Ramanujan Mathematical Society
Volume 38, Issue 1, March 2023 pp. 23–32.
Tilting correspondences of perfectoid rings
Authors:
Arnab Kundu
Author institution:
Université Paris-Saclay, Laboratoire de Mathématiques d’Orsay, F-91405, Orsay, France.
Summary:
In this article, we present an alternate proof of a vanishing result of
étale cohomology on perfectoid rings due to Cesnavicius 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.
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