Perfectoid Spaces
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Perfectoid Spaces
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Author : Debargha Banerjee
language : en
Publisher: Springer Nature
Release Date : 2022-04-21
Perfectoid Spaces written by Debargha Banerjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-21 with Mathematics categories.
This book contains selected chapters on perfectoid spaces, their introduction and applications, as invented by Peter Scholze in his Fields Medal winning work. These contributions are presented at the conference on “Perfectoid Spaces” held at the International Centre for Theoretical Sciences, Bengaluru, India, from 9–20 September 2019. The objective of the book is to give an advanced introduction to Scholze’s theory and understand the relation between perfectoid spaces and some aspects of arithmetic of modular (or, more generally, automorphic) forms such as representations mod p, lifting of modular forms, completed cohomology, local Langlands program, and special values of L-functions. All chapters are contributed by experts in the area of arithmetic geometry that will facilitate future research in the direction.
Perfectoid Spaces
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Author : Bhargav Bhatt
language : en
Publisher:
Release Date : 2019
Perfectoid Spaces written by Bhargav Bhatt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Topological fields categories.
Introduced 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 transformative impact perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields Medal in 2018. This book, originating from a series of lectures given at the 2017 Arizona Winter School on perfectoid spaces, provides a broad introduct.
Berkeley Lectures On P Adic Geometry
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Author : Peter Scholze
language : en
Publisher: Princeton University Press
Release Date : 2020-05-26
Berkeley Lectures On P Adic Geometry written by Peter Scholze and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-26 with Mathematics categories.
Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. 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. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
Almost Ring Theory
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Author : Ofer Gabber
language : en
Publisher: Springer
Release Date : 2003-12-09
Almost Ring Theory written by Ofer Gabber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-09 with Mathematics categories.
The authors develop thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring". Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions. The reader is assumed to be familiar with general categorical notions, some basic commutative algebra and some advanced homological algebra (derived categories, simplicial methods). Apart from these general prerequisites, the text is as self-contained as possible. One novel feature of the book - compared with Faltings' earlier treatment - is the systematic exploitation of the cotangent complex, especially for the study of deformations of almost algebras.
Arithmetic And Geometry
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Author : Gisbert Wüstholz
language : en
Publisher: Princeton University Press
Release Date : 2019-10-08
Arithmetic And Geometry written by Gisbert Wüstholz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-08 with Mathematics categories.
Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria—provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces. The second course, taught by Umberto Zannier, addresses the famous Pell equation—not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians. The third course, taught by Shou-Wu Zhang, originates in the Chowla–Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross–Zagier formula on Shimura curves and verify the Colmez conjecture on average.
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes
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Author : Boyan Sirakov
language : en
Publisher: World Scientific
Release Date : 2019-02-27
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Number Theory In Quantum Mechanics
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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :
Number Theory In Quantum Mechanics written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
"Number Theory in Quantum Mechanics" is a specialized exploration that bridges the realms of number theory and quantum mechanics. Catering to students, physicists, and researchers in quantum physics, this book investigates the intriguing connections between number theory concepts and quantum phenomena. Covering topics such as quantum states, operators, and wave functions, the book illuminates the mathematical underpinnings that emerge when applying number theory principles to quantum mechanics. With clarity and depth, this book serves as a valuable resource for those intrigued by the intersection of mathematical theory and quantum physics, offering new perspectives on the fundamental nature of quantum systems.
P Adic Differential Equations
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Author : Kiran S. Kedlaya
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-10
P Adic Differential Equations written by Kiran S. Kedlaya and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-10 with Mathematics categories.
Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
Women In Mathart
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Author : Shanna Dobson
language : en
Publisher: Springer Nature
Release Date : 2024-12-06
Women In Mathart written by Shanna Dobson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-06 with Mathematics categories.
This volume contains the proceedings from the first Women in MathArt Research Collaboration Conference for Women, showcasing women mathematicians researching and curating creative pedagogies at the intersection of mathematics and the arts. This volume contains contributions to mathart projects from student-mentor teams and researchers in all stages of their careers. The volume also contains survey articles on new mathart intersections such as neuroaesthetics, generative design, generative adversarial networks, and Langlands Program. New results of particular interest are: diamond Langlands; generative design in the geometrization of the local Langlands Program; investigations of the grammatology and visual epistemology of perfectoid diamonds in mathematics as grammatological metaphor; infinity-category constructions of pro-Generative Adversarial Networks; infinity-stackification of mathematical exigency; condensing temporal logic with entropic categorizations; perfectoid diamond holography; neuroaesthetics in immunology. Also included is the result to foster a more inclusive work community of mathematicians using the arts as a tool to bring more vulnerability and integrity to each individual's research life. Readers are herein provided a rigorous overview of current mathart developments and future mathart projects.
P Adic Hodge Theory Singular Varieties And Non Abelian Aspects
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Author : Bhargav Bhatt
language : en
Publisher: Springer Nature
Release Date : 2023-03-28
P Adic Hodge Theory Singular Varieties And Non Abelian Aspects written by Bhargav Bhatt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-28 with Mathematics categories.
This proceedings volume contains articles related to the research presented at the 2019 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning non-abelian aspects This volume contains both original research articles as well as articles that contain both new research as well as survey some of these recent developments.