Scholze algebraic geometry , all embed fully faithfully into the corresponding analytic category. Zuletzt geändert: September 2022, Peter Scholze. V4A2 - Algebraic Geometry II (Sommersemester 2017) Taught by Prof. Our plan was to learn the basics of algebraic geometry, so about sheaves, schemes, O X-modules, a ne/separated/proper morphisms, and eventually to show that proper normal curves over kcan be Arbeitsgruppe Arithmetische Geometrie und Darstellungstheorie in Bonn. The . Homepage of Peter Scholze Lecture (Summer 2022): Condensed Mathematics and Complex Geometry This course is joint with Dustin Clausen (University of Copenhagen) and will be held hybrid: On Tuesdays, 12:15 -- 14:00, Clausen will hold the lecture in Copenhagen and we will watch it in Room N0. Here’s the syllabus: The purpose of this course is to propose new foundations for analytic geometry. arXiv:1709. Subjects: Algebraic Geometry (math. View PDF Abstract: Peter Scholze obtained his PhD in 2012 under the supervision of Michael Rapoport at the Universität Bonn. Mar 21, 2024 · In the recent lecture series run jointly from IHÉS and Bonn, Clausen and Scholze have reworked—again—their foundations of geometry to focus attention on not arbitrary condensed sets and solid modules and so on, but the much smaller class of light condensed sets and so on. His concept of “perfectoid” spaces has helped solve several important and previously unsolved mathematical problems. Lectures on Analytic Geometry , lecture notes for course WS 19/20. Dr. The author always had the impression that the highly categorical techniques of algebraic geom- Algebraic Geometry I (archived link) as taught by Peter Scholze, notes by Jack Davies Algebraic Geometry II (archived link) as taught by Peter Scholze, notes by Jack Davies Algebraic Geometry I (archived link) as taught by Daniel Huybrechts, please try to refrain from crying out in horror upon looking at the reflex test Peter Scholze is an Algebraic Geometer at heart and many of his works focus on local aspects of p adic Algebraic Geometry. Condensed Mathematics and Complex Geometry, lecture notes for course SS 22. Introduction In August 2018, Scholze was awarded a Fields medal “for transforming arithmetic algebraic geometry over p-adic fields through his introduction of perfectoid spaces, He is known for his work on algebraic K-theory, on connections between homotopy theory and arithmetic, and more recently and jointly with Peter Scholze, on the development of condensed mathematics and the attendant approach to analytic geometry. We discuss recent developments in p-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for \compact p-adic manifolds" over new period maps on moduli spaces of abelian varieties to applications to the local and global Langlands This collaboration brings together mathematicians from a range of algebraic fields to study new ideas which have emerged over the last two decades in mixed characteristic algebraic geometry. We extend Stone duality to a fully faithful embedding of condensed sets into fpqc sheaves over an arbitrary field, which preserves colimits and finite limits. Feb 9, 2018 · Algebraic Geometry (math. He presented in a more compact form some of the previous fundamental theories pioneered by Gerd Faltings, Jean-Marc Fontaine and later by Kiran Kedlaya. " May 15, 2012 · Mathematics > Algebraic Geometry. Sep 21, 2017 · Mathematics > Algebraic Geometry. Specifically, we use the six-functor formalism for solid modules to define the skeletal filtration of a scheme, and then we show that decomposing a quasi-coherent sheaf with respect to this filtration gives rise to a new construction of the p-ADIC GEOMETRY PETER SCHOLZE Abstract. The topics covered are as follows: 1. Peter Scholze Typed by Jack Davies Peter Scholze is an Algebraic Geometer at heart and many of his works focus on local aspects of p adic Algebraic Geometry. Part of our goal is to develop foundations for analytic geometry that treat archimedean and non-archimedean geometry on equal grounds; and we will proceed by making archimedean geometry more similar to non-archimedean geometry. This is a survey article over some of the work of Peter Scholze for the Jahresbericht der DMV. Building on his discovery of perfectoid spaces, the author introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. 3 The relevance for algebraic geometry is furnished by the work of Bhatt-Morrow-Scholze which defines motivic filtrations on THH and related theories, and relates the graded pieces with p 𝑝 p-adic cohomology theories such as crystalline cohomology and the A inf subscript 𝐴 inf A_{\rm inf}-cohomology, cf. An unexpected feature of this cohomology is that in coordinates, it can be computed by a q-deformation of the de Rham complex, which is thus canonical, at least in the derived category. I called it algebraic geometry because that's how Scholze seems to refer to it at the beginning of his course notes. AG); K-Theory and Homology (math. Peter Scholze is a German mathematician. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. This makes complex geometry look more like Grothendieck-style algebraic geometry, with some analysis packaged into the foundations (analogously to the commutative algebra needed to set up AG), but once that's out of the way the proofs of some hard classical theorems look pretty formal. Geometrization of the local Langlands correspondence , lecture notes and videos. arXiv:1205. AG); Number Theory (math. These new ideas, which we broadly capture with the term “perfection”, include prismatic cohomology, perfectoid spaces, and the Cartier-Witt stack. Light condensed abelian groups. section 5. No originality is claimed. This course was taught in Bonn, Germany over the Wintersemester 2016/17, by Prof. May 26, 2020 · This book presents an important breakthrough in arithmetic geometry. He presented in a more compact form some of the previous fundamental theories pioneered by Gerd Faltings , Jean-Marc Fontaine and later by Kiran Kedlaya . Fair point. When appointing him as Germany’s youngest W3 Professor in 2012, the May 26, 2020 · In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. RT) How can one build algebraic geometry? One perspective is that one starts with the abelian category Ab of abelian groups, with its symmetric monoidal tensor product. We study how familiar notions from condensed mathematics/topology and algebraic geometry cor-respond to each other under this form of Stone Jun 6, 2016 · In recent work with Bhatt and Morrow, we defined a new integral p-adic cohomology theory interpolating between etale and de Rham cohomology. Peter Scholze. Analytic rings. In 2014, this book's author delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. In this short survey, we try to explain what we know about this In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Also, I only ever really learned how to take derivatives so if I see someone computing an Ext group in order to understand a space, the only thing I know to call this is "algebraic geometry. 3463 (math) View a PDF of the paper titled p-adic Hodge theory for rigid-analytic varieties, by Peter Scholze. These are enough to faithfully capture all sequential spaces, for 他提出了 状似完备空间 （ 英语 ： perfectoid space ） 理论，并在 动机 （ 英语 ： Motive (algebraic geometry) ） 理论和朗兰兹纲领这两个代数几何学的大方向上有杰出贡献。他于2018年获得菲尔兹奖，现任教于德国波恩大学 [5] 。 Oct 19, 2023 · Dustin Clausen and Peter Scholze are giving a course together this fall on Analytic Stacks, with Clausen lecturing at the IHES, Scholze from Bonn. NT); Representation Theory (math. 07343 (math) View a PDF of the paper titled Etale cohomology of diamonds, by Peter Scholze. 2. After working about the cohomology of Shimura varieties and the Langlands program, his PhD thesis was about a theory of perfectoid spaces, which gives a method to compare objects in mixed characteristic with objects in equal characteristic p, with […] of proof used to prove the corresponding result in p-adic geometry (known as \Tate acyclicity"). 008 at the University, while Thursdays, 12:15 -- 14:00 May 26, 2020 · In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p -adic geometry. After working about the cohomology of Shimura varieties and the Langlands program, his PhD thesis was about a theory of perfectoid spaces, which gives a method to compare objects in mixed characteristic with objects in equal characteristic p, with […] Peter Scholze obtained his PhD in 2012 under the supervision of Michael Rapoport at the Universität Bonn. KT); Number Theory From: Peter Scholze Fri, 9 Feb 2018 13:57:42 UTC (85 KB) [v2] Tue, 9 Jan 8, 2024 · AND ALGEBRAIC GEOMETRY ROK GREGORIC Abstract. Mar 13, 2024 · In this paper, we apply Clausen-Scholze's theory of solid modules to the existence of adelic decompositions for schemes of finite type over $\\mathbb{Z}$. Peter Scholze examines the overlap between arithmetic algebraic geometry and the theory of automorphic forms. (3)strictly generalizes algebraic geometry in the sense that the category of schemes, the theory of quasicoherent sheaves over them, etc. rciqk gfnh rob fbyba jquna pargs cmdmp nqpvf ngncydks qzdyt