Peter scholze perfectoid spaces
WebSummary. We develop an analytic theory of cusps for Scholze's p -adic modular curves at infinite level in terms of perfectoid parameter spaces for Tate curves. As an application, we describe a canonical tilting isomorphism between an anticanonical overconvergent neighbourhood of the ordinary locus of the modular curve at level Γ 1 ( p ∞) and ...
Peter scholze perfectoid spaces
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WebTitle: Perfectoid spaces : lectures from the 2024 Arizona Winter School / Bhargav Bhatt [and threeothers];withanIntroductionbyPeterScholze;BrydenCais,editor. Description: … WebIn recognition of the transformative impact perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields Medal in 2024. This book, originating …
WebFormalising perfectoid spaces Kevin Buzzard ∗ Johan Commelin † Patrick Massot ‡ May 29, 2024 Abstract Perfectoid spaces are sophisticated objects in arithmetic geometry introduced by Peter Scholze in 2012. We formalised enough de˙nitions and theorems in topology, algebra and geometry to de˙ne perfectoid spaces in the Lean theorem prover. WebWe establish various properties of the p -adic algebraic K -theory of smooth algebras over perfectoid rings living over perfectoid valuation rings. In particular, the p -adic K -theory of …
WebIn recognition of the transformative impact perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields Medal in 2024. This book, originating from a series of lectures given at the 2024 Arizona Winter School on perfectoid spaces, provides a broad introduction to the subject. WebWe explained Peter Scholze’s definition of perfectoid spaces to computers, using the Lean theorem prover, mainly developed at Microsoft Research by Leonardo de Moura. Building …
WebTHE WORK OF PETER SCHOLZE M. RAPOPORT Abstract. He has developed powerful methods in algebraic geometry over p-adic fields, and has proved striking theorems in this area. My purpose here is to convey some idea of the accomplishments of Peter Scholze for which he was awarded the Fields medal.
WebLes jeudis 6, 13 et 20 Octobre, le mercredi 26 Octobre et les jeudis 3 et 10 Novembre 2011 de 14h30 à 16h30 Peter Scholze (Universität Bonn) Perfectoid Spaces and the Weight-Monodromy Conjecture We will introduce the notion of perfectoid spaces. nrf s 26Web13. apr 2024 · This activity continues: Peter Scholze’s perfectoid spaces and condensed mathematics are examples of new directions of this kind, too new to make it into these volumes. Of all of these ideas, the ones that at the moment I find most compelling are the twistor geometry ideas of Roger Penrose, and I’ll have much more to say about those in ... night light working only on one screenWebIntroduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry in characteristic 0 and characteristic \(p\), and have been used to solve many important problems, including cases of the weight-monodromy conjecture and the association of Galois representations to torsion classes in cohomology. In recognition of the ... nrf s.26WebAndrej Vukovic, Department of Pure Mathematics, University of Waterloo "Perfectoid Spaces, Diamonds, and Applications" I explain Peter Scholze's concepts of perfectoid spaces and diamonds, then describe some applications to the Langlands program. This seminar will be held both online and in person: Room: MC 4058 (note different room) Zoom link: nrf rx8WebIn addition, Scholze extended the foundational results of p-adic Hodge theory to a new setting. That such an extension should be possible was conjectured by Tate in 1966. … night like this crowderWeb21. nov 2011 · Perfectoid Spaces. We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings’ almost purity theorem, and for … nrf s 36WebThis book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key ... nrf s.38