2016/02/29 by Kiran S. Kedlaya, Kedlaya, Kiran S.
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1602.09016
openalex publication_date 2016/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The ring of Witt vectors over a perfect valuation ring of characteristic p, often denoted Ainf, plays a pivotal role in p-adic Hodge theory; for instance, Bhatt, Morrow, and Scholze have recently reinterpreted and refined the crystalline comparison isomorphism by relating it to a certain Ainf-valued cohomology theory. We address some basic ring-theoretic questions about Ainf motivated by analogies with two-dimensional regular local rings. For example, we show that in most cases Ainf, which is manifestly not noetherian, is also not coherent. On the other hand, it does have the property that vector bundles over the complement of the closed point in Spec Ainf do extend uniquely over the puncture; moreover, a similar statement holds in Huber's category of adic spaces.