Classification of Pseudo-reductive Groups (AM-191)


Author: Brian Conrad,Gopal Prasad
Publisher: Princeton University Press
ISBN: 1400874025
Category: Mathematics
Page: 256
View: 6979

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In the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study the classification over an arbitrary field. An isomorphism theorem proved here determines the automorphism schemes of these groups. The book also gives a Tits-Witt type classification of isotropic groups and displays a cohomological obstruction to the existence of pseudo-split forms. Constructions based on regular degenerate quadratic forms and new techniques with central extensions provide insight into new phenomena in characteristic 2, which also leads to simplifications of the earlier work. A generalized standard construction is shown to account for all possibilities up to mild central extensions. The results and methods developed in Classification of Pseudo-reductive Groups will interest mathematicians and graduate students who work with algebraic groups in number theory and algebraic geometry in positive characteristic.

Algebraic Groups: Structure and Actions


Author: Mahir Bilen Can
Publisher: American Mathematical Soc.
ISBN: 1470426013
Category: Algebraic geometry -- Algebraic groups -- Group schemes
Page: 294
View: 1216

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This volume contains the proceedings of the 2015 Clifford Lectures on Algebraic Groups: Structures and Actions, held from March 2–5, 2015, at Tulane University, New Orleans, Louisiana. This volume consists of six articles on algebraic groups, including an enhanced exposition of the classical results of Chevalley and Rosenlicht on the structure of algebraic groups; an enhanced survey of the recently developed theory of pseudo-reductive groups; and an exposition of the recently developed operational -theory for singular varieties. In addition, there are three research articles containing previously unpublished foundational results on birational automorphism groups of algebraic varieties; solution of Hermite-Joubert problem over -closed fields; and cohomological invariants and applications to classifying spaces. The old and new results presented in these articles will hopefully become cornerstones for the future development of the theory of algebraic groups and applications. Graduate students and researchers working in the fields of algebraic geometry, number theory, and representation theory will benefit from this unique and broad compilation of fundamental results on algebraic group theory.

Descent in Buildings (AM-190)


Author: Bernhard Mühlherr,Holger P. Petersson,Richard M. Weiss
Publisher: Princeton University Press
ISBN: 1400874017
Category: Mathematics
Page: 352
View: 9166

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Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a "residually pseudo-split" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms. This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.

Pseudo-reductive Groups


Author: Brian Conrad,Ofer Gabber,Gopal Prasad
Publisher: Cambridge University Press
ISBN: 1139490346
Category: Mathematics
Page: N.A
View: 9021

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Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This self-contained monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. The authors present numerous new results and also give a complete exposition of Tits' structure theory of unipotent groups. They prove the conjugacy results (conjugacy of maximal split tori, minimal pseudo-parabolic subgroups, maximal split unipotent subgroups) announced by Armand Borel and Jacques Tits, and also give the Bruhat decomposition, of general smooth connected algebraic groups. Researchers and graduate students working in any related area, such as algebraic geometry, algebraic group theory, or number theory, will value this book as it develops tools likely to be used in tackling other problems.

On Certain L-functions

Conference on Certain L-functions in Honor of Freydoon Shahidi, July 23-27, 2007, Purdue University, West Lafayette, Indiana
Author: James Arthur
Publisher: American Mathematical Soc.
ISBN: 0821852043
Category: Mathematics
Page: 647
View: 1059

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This volume constitutes the proceedings of a conference, ``On Certain $L$-functions'', held July 23-27, 2007 at Purdue University, West Lafayette, Indiana. The conference was organized in honor of the 60th birthday of Freydoon Shahidi, widely recognized as having made groundbreaking contributions to the Langlands program. The articles in this volume represent a snapshot of the state of the field from several viewpoints. Contributions illuminate various areas of the study of geometric, analytic, and number theoretic aspects of automorphic forms and their $L$-functions, and both local and global theory are addressed. Topics discussed in the articles include Langlands functoriality, the Rankin-Selberg method, the Langlands-Shahidi method, motivic Galois groups, Shimura varieties, orbital integrals, representations of $p$-adic groups, Plancherel formula and its consequences, the Gross-Prasad conjecture, and more. The volume also includes an expository article on Shahidi's contributions to the field, which serves as an introduction to the subject. Experts will find this book a useful reference, and beginning researchers will be able to use it to survey major results in the Langlands program.

Expansion in Finite Simple Groups of Lie Type


Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 1470421968
Category: Mathematics
Page: 303
View: 3685

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Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.

His One and Only Bride


Author: Tara Randel
Publisher: Harlequin
ISBN: 1488084890
Category: Fiction
Page: 368
View: 4037

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He never thought he’d see her again! After being reported missing, presumed dead, globe-hopping photojournalist Mitch Simmons never thought he’d see his estranged wife, Zoe, again. Yet here he is back in their coastal Florida town, where Zoe is mayor. Turns out she isn’t the only one he left behind. Discovering he has a baby son awakens thrilling new emotions in Mitch. And there are his still-powerful feelings for the high school sweetheart he vowed to love and honor forever. Thankfully, they’ll have the chance to find the love that was always there…

The Endoscopic Classification of Representations Orthogonal and Symplectic Groups


Author: James Arthur
Publisher: American Mathematical Soc.
ISBN: 0821849905
Category: Mathematics
Page: 590
View: 2804

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Within the Langlands program, endoscopy is a fundamental process for relating automorphic representations of one group with those of another. In this book, Arthur establishes an endoscopic classification of automorphic representations of orthogonal and symplectic groups . The representations are shown to occur in families (known as global -packets and -packets), which are parametrized by certain self-dual automorphic representations of an associated general linear group . The central result is a simple and explicit formula for the multiplicity in the automorphic discrete spectrum of for any representation in a family. The results of the volume have already had significant applications: to the local Langlands correspondence, the construction of unitary representations, the existence of Whittaker models, the analytic behaviour of Langlands -functions, the spectral theory of certain locally symmetric spaces, and to new phenomena for symplectic epsilon-factors. One can expect many more. In fact, it is likely that both the results and the techniques of the volume will have applications to almost all sides of the Langlands program. The methods are by comparison of the trace formula of with its stabilization (and a comparison of the twisted trace formula of with its stabilization, which is part of work in progress by Moeglin and Waldspurger). This approach is quite different from methods that are based on -functions, converse theorems, or the theta correspondence. The comparison of trace formulas in the volume ought to be applicable to a much larger class of groups. Any extension at all will have further important implications for the Langlands program.

Linear Algebraic Monoids


Author: Lex Renner
Publisher: Springer Science & Business Media
ISBN: 3540275568
Category: Mathematics
Page: 246
View: 2571

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This solid volume discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. Open problems are discussed as they arise and many useful exercises are included.

Analysis and Algebra on Differentiable Manifolds

A Workbook for Students and Teachers
Author: Pedro M. Gadea,Jaime Muñoz Masqué,Ihor V. Mykytyuk
Publisher: Springer Science & Business Media
ISBN: 9400759525
Category: Mathematics
Page: 618
View: 2995

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This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear. A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics. In this 2nd edition: • 76 new problems • a section devoted to a generalization of Gauss’ Lemma • a short novel section dealing with some properties of the energy of Hopf vector fields • an expanded collection of formulae and tables • an extended bibliography Audience This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.

Grothendieck-Serre Correspondence


Author: Alexandre Grothendieck,Pierre Colmez,Jean Pierre Serre
Publisher: American Mathematical Soc.
ISBN: 082183424X
Category: Mathematics
Page: 576
View: 4137

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The book is a bilingual (French and English) edition of the mathematical correspondence between A. Grothendieck and J-P. Serre. The original French text of 84 letters is supplemented here by the English translation, with French text printed on the left-hand pages and the corresponding English text printed on the right-hand pages. The book also includes several facsimiles of original letters. The letters presented in the book were mainly written between 1955 and 1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. The reader can follow the creation of some of the most important notions of modern mathematics, like sheaf cohomology, schemes, Riemann-Roch type theorems, algebraic fundamental group, motives. The letters also reflect the mathematical and political atmosphere of this period (Bourbaki, Paris, Harvard, Princeton, war in Algeria, etc.). Also included are a few letters written between 1984 and 1987. The letters are supplemented by J-P. Serre's notes, which give explanations, corrections, and references further results. The book should be useful to specialists in algebraic geometry, in history of mathematics, and to all mathematicians who want to understand how great mathematics is created.

Modules Over Non-Noetherian Domains


Author: László Fuchs,Luigi Salce
Publisher: American Mathematical Soc.
ISBN: 0821819631
Category: Mathematics
Page: 613
View: 515

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In this book, the authors present both traditional and modern discoveries in the subject area, concentrating on advanced aspects of the topic. Existing material is studied in detail, including finitely generated modules, projective and injective modules, and the theory of torsion and torsion-free modules. Some topics are treated from a new point of view. Also included are areas not found in current texts, for example, pure-injectivity, divisible modules, uniserial modules, etc. Special emphasis is given to results that are valid over arbitrary domains. The authors concentrate on modules over valuation and Prufer domains, but also discuss Krull and Matlis domains, $h$-local, reflexive, and coherent domains. The volume can serve as a standard reference book for specialists working in the area and also is a suitable text for advanced-graduate algebra courses and seminars.

Software Studies

A Lexicon
Author: Matthew Fuller
Publisher: MIT Press
ISBN: 0262062747
Category: Computers
Page: 334
View: 8113

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A cultural field guide to software: artists, computer scientists, designers, cultural theorists, programmers, and others define a new field of study and practice.

Alkaloids - Secrets of Life:

Aklaloid Chemistry, Biological Significance, Applications and Ecological Role
Author: Tadeusz Aniszewski
Publisher: Elsevier
ISBN: 9780080475332
Category: Science
Page: 334
View: 7055

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Alkaloids, represent a group of interesting and complex chemical compounds, produced by the secondary metabolism of living organisms in different biotopes. They are relatively common chemicals in all kingdoms of living organisms in all environments. Two hundred years of scientific research has still not fully explained the connections between alkaloids and life. Alkaloids-Chemistry, Biological Significance, Applications and Ecological Role provides knowledge on structural typology, biosynthesis and metabolism in relation to recent research work on alkaloids. Considering an organic chemistry approach to alkaloids using biological and ecological explanation. Within the book several questions that persist in this field of research are approached as are some unresearched areas. The book provides beneficial text for an academic and professional audience and serves as a source of knowledge for anyone who is interested in the fascinating subject of alkaloids. Each chapter features an abstract. Appendices are included, as are a listing of alkaloids, plants containing alkaloids and some basic protocols of alkaloid analysis. * Presents the ecological role of alkaloids in nature and ecosystems * Interdisciplinary and reader friendly approach * Up-to-date knowledge

New Challenges to Philosophy of Science


Author: Hanne Andersen,Dennis Dieks,Wenceslao J. Gonzalez,Thomas Uebel,Gregory Wheeler
Publisher: Springer Science & Business Media
ISBN: 9400758456
Category: Science
Page: 512
View: 3092

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This volume is a serious attempt to open up the subject of European philosophy of science to real thought, and provide the structural basis for the interdisciplinary development of its specialist fields, but also to provoke reflection on the idea of ‘European philosophy of science’. This efforts should foster a contemporaneous reflection on what might be meant by philosophy of science in Europe and European philosophy of science, and how in fact awareness of it could assist philosophers interpret and motivate their research through a stronger collective identity. The overarching aim is to set the background for a collaborative project organising, systematising, and ultimately forging an identity for, European philosophy of science by creating research structures and developing research networks across Europe to promote its development.

Degrowth

A Vocabulary for a New Era
Author: Giacomo D'Alisa,Federico Demaria,Giorgos Kallis
Publisher: Routledge
ISBN: 1134449771
Category: Business & Economics
Page: 220
View: 7010

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Degrowth is a rejection of the illusion of growth and a call to repoliticize the public debate colonized by the idiom of economism. It is a project advocating the democratically-led shrinking of production and consumption with the aim of achieving social justice and ecological sustainability. This overview of degrowth offers a comprehensive coverage of the main topics and major challenges of degrowth in a succinct, simple and accessible manner. In addition, it offers a set of keywords useful forintervening in current political debates and for bringing about concrete degrowth-inspired proposals at different levels - local, national and global. The result is the most comprehensive coverage of the topic of degrowth in English and serves as the definitive international reference. More information at: vocabulary.degrowth.org View the author spotlight featuring events and press related to degrowth at http://t.co/k9qbQpyuYp.

The Geometry of Algebraic Cycles

Proceedings of the Conference on Algebraic Cycles, Columbus, Ohio, March 25-29, 2008
Author: Reza Akhtar,Patrick Brosnan,Roy Joshua
Publisher: American Mathematical Soc.
ISBN: 0821851918
Category: Mathematics
Page: 187
View: 5263

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The subject of algebraic cycles has its roots in the study of divisors, extending as far back as the nineteenth century. Since then, and in particular in recent years, algebraic cycles have made a significant impact on many fields of mathematics, among them number theory, algebraic geometry, and mathematical physics. The present volume contains articles on all of the above aspects of algebraic cycles. It also contains a mixture of both research papers and expository articles, so that it would be of interest to both experts and beginners in the field.

The Finiteness Obstruction of C. T. C. Wall


Author: Kalathoor Varadarajan
Publisher: Wiley-Interscience
ISBN: N.A
Category: Mathematics
Page: 194
View: 2469

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This monograph gives an account of C. T. C. Wall's work on finiteness conditions on CW-complexes. Varadarayan recasts Wall's obstruction proofs in algebraic terms (the proofs depending upon results from algebraic number theory and on K-theoretic induction theorems), and ends with a study of finitely-dominated nilpotent spaces. Most of the material in this volume appears for the first time in book form.