Motivic Integration And Its Interactions With Model Theory And Non Archimedean Geometry
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| Author | : Raf Cluckers |
| Publisher | : Cambridge University Press |
| Total Pages | : 347 |
| Release | : 2011-09-22 |
| Genre | : Mathematics |
| ISBN | : 1139499793 |
Assembles different theories of motivic integration for the first time, providing all of the necessary background for graduate students and researchers from algebraic geometry, model theory and number theory. In a rapidly-evolving area of research, this volume and Volume 2, which unite the several viewpoints and applications, will prove invaluable.
| Author | : Raf Cluckers |
| Publisher | : |
| Total Pages | : 334 |
| Release | : 2011 |
| Genre | : Analytic spaces |
| ISBN | : 9781139140829 |
"The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This first volume contains introductory texts on the model theory of valued fields, different approaches to non-Archimedean geometry, and motivic integration on algebraic varieties and non-Archimedean spaces"--
| Author | : Raf Cluckers |
| Publisher | : |
| Total Pages | : 250 |
| Release | : 2011 |
| Genre | : Geometry, Algebraic |
| ISBN | : 9781139141154 |
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.
| Author | : Kazuaki Taira |
| Publisher | : Cambridge University Press |
| Total Pages | : 348 |
| Release | : 2016-04-28 |
| Genre | : Mathematics |
| ISBN | : 1316620867 |
This second edition explores the relationship between elliptic and parabolic initial boundary value problems, for undergraduate and graduate students.
| Author | : Simon R. Blackburn |
| Publisher | : Cambridge University Press |
| Total Pages | : 387 |
| Release | : 2013-06-27 |
| Genre | : Mathematics |
| ISBN | : 1107276934 |
This volume contains nine survey articles based on the invited lectures given at the 24th British Combinatorial Conference, held at Royal Holloway, University of London in July 2013. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, matroid theory and automatic counting, as well as connections to coding theory and Bent functions. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of cutting-edge developments. The book provides a valuable survey of the present state of knowledge in combinatorics, and will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.
| Author | : Grant Walker |
| Publisher | : Cambridge University Press |
| Total Pages | : 371 |
| Release | : 2018 |
| Genre | : Mathematics |
| ISBN | : 1108414486 |
The first of two volumes covering the Steenrod algebra and its various applications. Suitable as a graduate text.
| Author | : John Coates |
| Publisher | : Cambridge University Press |
| Total Pages | : 317 |
| Release | : 2015-03-19 |
| Genre | : Mathematics |
| ISBN | : 1316241300 |
There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings.
| Author | : Grant Walker (Mathematician) |
| Publisher | : Cambridge University Press |
| Total Pages | : 381 |
| Release | : 2018 |
| Genre | : Polynomials |
| ISBN | : 1108414451 |
This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's 'hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n,F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
| Author | : Pieter Belmans |
| Publisher | : Cambridge University Press |
| Total Pages | : 307 |
| Release | : 2022-10-31 |
| Genre | : Mathematics |
| ISBN | : 1009054856 |
A collection of expository articles on modern topics in algebraic geometry, focusing on the geometry of algebraic spaces and stacks.
| Author | : Grant Walker |
| Publisher | : Cambridge University Press |
| Total Pages | : 381 |
| Release | : 2017-11-09 |
| Genre | : Mathematics |
| ISBN | : 1108355927 |
This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's `hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n, F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
