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Author: Bhargav Bhatt
Publisher:
ISBN: 9782856299371
Category :
Languages : en
Pages : 165
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Book Description
Author: Bhargav Bhatt
Publisher:
ISBN: 9782856299371
Category :
Languages : en
Pages : 165
Get Book Here
Book Description
Author: Bhargav Bhatt
Publisher: American Mathematical Society
ISBN: 1470465108
Category : Mathematics
Languages : en
Pages : 297
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Book Description
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 introduction to the subject. After an introduction with insight into the history and future of the subject by Peter Scholze, Jared Weinstein gives a user-friendly and utilitarian account of the theory of adic spaces. Kiran Kedlaya further develops the foundational material, studies vector bundles on Fargues–Fontaine curves, and introduces diamonds and shtukas over them with a view toward the local Langlands correspondence. Bhargav Bhatt explains the application of perfectoid spaces to comparison isomorphisms in $p$-adic Hodge theory. Finally, Ana Caraiani explains the application of perfectoid spaces to the construction of Galois representations associated to torsion classes in the cohomology of locally symmetric spaces for the general linear group. This book will be an invaluable asset for any graduate student or researcher interested in the theory of perfectoid spaces and their applications.
Author: Helge Holden
Publisher: Springer
ISBN: 3319990284
Category : Mathematics
Languages : en
Pages : 774
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Book Description
The book presents the winners of the Abel Prize in mathematics for the period 2013–17: Pierre Deligne (2013); Yakov G. Sinai (2014); John Nash Jr. and Louis Nirenberg (2015); Sir Andrew Wiles (2016); and Yves Meyer (2017). The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos for the period 2003–2017 showing many of the additional activities connected with the Abel Prize. As an added feature, video interviews with the Laureates as well as videos from the prize ceremony are provided at an accompanying website (http://extras.springer.com/). This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer 2014), which profile the work of the previous Abel Prize winners.
Author: Edward Frenkel
Publisher: Cambridge University Press
ISBN: 0521854431
Category : Mathematics
Languages : en
Pages : 5
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Book Description
The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Author: Dennis P. Sullivan
Publisher: Springer
ISBN: 9789048103508
Category : Mathematics
Languages : en
Pages : 286
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Book Description
The seminal ‘MIT notes’ of Dennis Sullivan were issued in June 1970 and were widely circulated at the time. The notes had a - jor in?uence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including p-local, pro?nite and rational homotopy theory, le- ing to the solution of the Adams conjecture on the relationship between vector bundles and spherical ?brations, the formulation of the ‘Sullivan conjecture’ on the contractibility of the space of maps from the classifying space of a ?nite group to a ?nite dimensional CW complex, theactionoftheGalois groupoverQofthealgebraicclosureQof Q on smooth manifold structures in pro?nite homotopy theory, the K-theory orientation ofPL manifolds and bundles. Some of this material has been already published by Sullivan him- 1 self: in an article in the Proceedings of the 1970 Nice ICM, and in the 1974 Annals of Mathematics papers Genetics of homotopy theory and the Adams conjecture and The transversality character- 2 istic class and linking cycles in surgery theory . Many of the ideas originating in the notes have been the starting point of subsequent 1 reprinted at the end of this volume 2 joint with John Morgan vii viii 3 developments . However, the text itself retains a unique ?avour of its time, and of the range of Sullivan’s ideas.
Author: Jean-Pierre Serre
Publisher: CRC Press
ISBN: 1466501936
Category : Mathematics
Languages : en
Pages : 169
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Book Description
Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic cohomology and group representations, presented in
Author: Angela Mendonca
Publisher: Springer Science & Business Media
ISBN: 9400713215
Category : Science
Languages : en
Pages : 209
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Book Description
Shortly, this book is the written up-graded version of the topics discussed during the Small Meeting of the 2nd International School Congress: Natural Resources, Sustainability and Humanity, held in Braga, Portugal, 5-8 May 2010 with the diverse participation of scientists, educators and governmental representatives. The Earth hosts an immense ecosystem, colonized by millions of species for billions of years but only for a few tens of thousands of years by humans. Environmental history tells though that it was humankind that shaped the environment as no other species. History, geography, religion and politics among other reasons have differentiated populations with respect to access to safe food and water, education, health, and to space and natural resource utilization. The globalization era of trade, information and communication is shortening distances and increasing overall wealth, but, as is pointed out in this book, it is also contributing to the propagation of diseases, and to the modification or even destruction of native ecosystems by exotic invasive species. Man is the only species that has the perception of its history, evolution, of the consequences of its decisions, and that there is a future ahead. It is also the only species that has the potential to change it. This awareness can be a source of anxiety and contradictory behaviours, but it is also the key to changing attitudes towards the construction of a common sustainable home, by committed education, interdisciplinary approaches, mobilization and empowerment of people and political consonant actions.
Author: Bertfried Fauser
Publisher: Springer Science & Business Media
ISBN: 376438736X
Category : Science
Languages : en
Pages : 436
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Book Description
The present volume emerged from the 3rd `Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics.
Author: Alexandru Buium
Publisher: American Mathematical Soc.
ISBN: 147043623X
Category : Mathematics
Languages : en
Pages : 357
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Book Description
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Author: Dennis Gaitsgory
Publisher: Princeton University Press
ISBN: 0691184437
Category : Mathematics
Languages : en
Pages : 320
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Book Description
A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil’s conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of Weil’s conjecture, based on the geometry of the moduli stack of G-bundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting l-adic sheaves. Using this theory, Dennis Gaitsgory and Jacob Lurie articulate a different local-to-global principle: a product formula that expresses the cohomology of the moduli stack of G-bundles (a global object) as a tensor product of local factors. Using a version of the Grothendieck-Lefschetz trace formula, Gaitsgory and Lurie show that this product formula implies Weil’s conjecture. The proof of the product formula will appear in a sequel volume.
