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Peter scholze perfectoid spaces

WebBackground. Perfectoid spaces are a class of spaces in p-adic arithmetic geometry introduced in 2012 by Peter Scholze in his PhD thesis. Very roughly speaking, these spaces are modeled by (spectra attached to) Z p-algebras whose mod p reductions have all p-power roots. Despite their youth, these spaces have had stunning applications to WebIn this school, we intend to understand connections between the arithmetic theory of modular forms and new developments in p-adic Hodge theory that grew from the breakthrough work of Peter Scholze on perfectoid spaces (see P. Scholze "Perfectoid spaces" Publ. Math. de l’IHES 116 (2012)). p-adic methods play a key role in the study of ...

Formalising perfectoid spaces - arXiv

Web23. jan 2024 · Perfectoid spaces are this year's subject for the Arizona Winter School (link) and, as preparation, I am currently trying to understand the subject better. ... Apart from all the written sources, there are six videos of Peter Scholze's lectures at the IHÉS in 2011 on Perfectoid Spaces and the Weight-Monodromy Conjecture : WebPERFECTOID SPACES PETER SCHOLZE Abstract. We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings’ almost purity … phil beadle teacher https://anywhoagency.com

What is a brief description of Peter Scholze

Web10. aug 2012 · P. Scholze, p-adic Hodge theory for rigid-analytic varieties, arXiv:1205.3463, 2012. S. W. Shin, Galois representations arising from some compact Shimura varieties, … 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 … Web1. aug 2024 · Scholze continues to explore perfectoid spaces, but he has also branched out into other areas of mathematics touching on algebraic topology, which uses algebra to study shapes. “Over the course of the last year and a half, Peter has become a complete master of the subject,” Bhatt said. “He changed the way [the experts] think about it.” phil beadle the unteachables

Peter SCHOLZE (oct 2011) - 1/6 Perfectoid Spaces and the Weight ...

Category:Perfectoid Spaces - American Mathematical Society

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Peter scholze perfectoid spaces

[1303.5948] Perfectoid Spaces: A survey - arXiv.org

Webmath.uni-bonn.de…. Peter Scholze ( Dresden, 11 de desembre de 1987) és un matemàtic alemany conegut pels seus treballs en geometria algebraic a. És professor a la Universitat de Bonn i es considera un dels matemàtics actuals més influents. [1] [2] [3] 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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Web22. jan 2024 · Perfectoid spaces are sophisticated objects in arithmetic geometry introduced by Peter Scholze in 2012. We formalised enough definitions and theorems in topology, algebra and geometry to define perfectoid spaces in the Lean theorem prover. This experiment confirms that a proof assistant can handle complexity in that direction, which … WebThis book contains selected chapters on perfectoid spaces, their introduction and applications, as invented by Peter Scholze in his Fields Medal winning work. These …

WebPeter Scholze ( German pronunciation: [ˈpeːtɐ ˈʃɔlt͡sə] ( listen); born 11 December 1987 [2]) is a German mathematician known for his work in arithmetic geometry. He has been a professor at the University of Bonn …

Web27. okt 2024 · Perfectoid spaces are sophisticated objects in arithmetic geometry introduced by Peter Scholze in 2012. We formalised enough definitions and theorems in … WebPeter Scholze (* 11. Dezember 1987 in Dresden) ist ein vielfach ausgezeichneter deutscher Mathematiker und Träger der Fields-Medaille. ... in drei Semestern und das Master …

Web17. júl 2024 · Peter SCHOLZE (oct 2011) - 1/6 Perfectoid Spaces and the Weight-Monodromy Conjecture Institut des Hautes Études Scientifiques (IHÉS) 54.2K subscribers 27K views 4 years ago We …

WebIn 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. … phil bealWebTHE WORK OF PETER SCHOLZE 3 (ii) For any perfectoid space X, the structure pre-sheaf OX is a sheaf and, if X is affinoid perfectoid, then Hi ´et(X,OX) = 0 for i>0 . The first part of the theorem is Scholze’s tilting equivalence for perfectoid spaces, which simultaneously extends the Fontaine-Wintenberger theorem and the almost phil beale barclaysPERFECTOID SPACES PETER SCHOLZE Abstract. We introduce a certain class of … Authors: Peter Scholze. Download PDF Abstract: We introduce a certain class of … phil beal spursWebPerfectoid spaces may be used to (and were invented in order to) compare mixed characteristic situations with purely finite characteristic ones. Technical tools for making … phil beamer calhoun gaWebPerfectoid spaces - Peter Scholze - YouTube Peter ScholzeUniversity of BonnMarch 22, 2011For more videos, visit http://video.ias.edu Peter ScholzeUniversity of BonnMarch 22, … phil beale aldermoreWeb1. okt 2024 · Introduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry in characteristic 0 and characteristic p, and … phil bean artistWebWe 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 … phil beales