Purity for flat cohomology. mpim-bonn. Show the cohomological semi-purity using perfectoid spaces [CS, Theorem 3. As far as I understand, the theorem has been proved by Gabber in at least two ways. 1. One explains how to obtain the full cohomological purity from a similar argument [CS, Remark 3. Dec 23, 2019 ยท View a PDF of the paper titled Purity for flat cohomology, by Kestutis Cesnavicius and Peter Scholze For the proof, we reduce to a flat purity statement for perfectoid rings, establish $p$-complete arc descent for flat cohomology of perfectoids, and then relate to coherent cohomology of $\mathbb {A}_ {\mathrm {Inf}}$ via prismatic Dieudonné theory. 6. 9. de Abstract We establish the flat cohomology version of the Gabber--Thomason purity for étale cohomology: for a complete intersection Noetherian local ring (R,m) (R, m) and a commutative, finite, flat R R -group G G, the flat cohomology Hi m(R,G) H m i (R, G) vanishes for i<dim(R) i <d i m (R). See full list on people. The following continuity formula, among other things, computes the flat cohomology of complete Noetherian local rings with commutative, finite, flat group coefficients and has consequences for invariance of flat cohomology under Henselian pairs, see Example 5. 3]. There are several other ways to state the result: chapter 16 of Milne's online Lectures on Etale Cohomology explains nicely how to go between them. 7 and Corollary 5. 4]. . mpg. zjnxs ftbtu wbagcvz vjxwgqd tgz lhxcnd bgkpbtgp fpdhwp bzmv afrrcq