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Etale Homotopy of Simplicial Schemes. (AM-104), Volume 104
This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications of this theory to algebraic topology, finite Chevalley groups, and algebraic geometry. Of particular interest are the discussions concerning the Adams Conjecture, K-theories of finite fields, and Poincare duality. Because these applications have required repeated modifications of the original formulation of etale homotopy theory, the author provides a new treatment of the foundations which is more general and more precise than previous versions. One purpose of this book is to offer the basic techniques and results of etale homotopy theory to topologists and algebraic geometers who may then apply the theory in their own work. With a view to such future applications, the author has introduced a number of new constructions (function complexes, relative homology and cohomology, generalized cohomology) which have immediately proved applicable to algebraic K-theory.
Cycles, Transfers, and Motivic Homology Theories. (AM-143)
The original goal that ultimately led to this volume was the construction of "motivic cohomology theory," whose existence was conjectured by A. Beilinson and S. Lichtenbaum. This is achieved in the book's fourth paper, using results of the other papers whose additional role is to contribute to our understanding of various properties of algebraic cycles. The material presented provides the foundations for the recent proof of the celebrated "Milnor Conjecture" by Vladimir Voevodsky. The theory of sheaves of relative cycles is developed in the first paper of this volume. The theory of presheaves with transfers and more specifically homotopy invariant presheaves with transfers is the main theme of the second paper. The Friedlander-Lawson moving lemma for families of algebraic cycles appears in the third paper in which a bivariant theory called bivariant cycle cohomology is constructed. The fifth and last paper in the volume gives a proof of the fact that bivariant cycle cohomology groups are canonically isomorphic (in appropriate cases) to Bloch's higher Chow groups, thereby providing a link between the authors' theory and Bloch's original approach to motivic (co-)homology.
Handbook of K-Theory
This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.
Categorical, Combinatorial and Geometric Representation Theory and Related Topics
This book is the third Proceedings of the Southeastern Lie Theory Workshop Series covering years 2015–21. During this time five workshops on different aspects of Lie theory were held at North Carolina State University in October 2015; University of Virginia in May 2016; University of Georgia in June 2018; Louisiana State University in May 2019; and College of Charleston in October 2021. Some of the articles by experts in the field describe recent developments while others include new results in categorical, combinatorial, and geometric representation theory of algebraic groups, Lie (super) algebras, and quantum groups, as well as on some related topics. The survey articles will be beneficial to junior researchers. This book will be useful to any researcher working in Lie theory and related areas.
An Alpine Expedition through Algebraic Topology
This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. The papers in this volume cover topics such as category theory and homological algebra, functor homology, algebraic -theory, cobordism categories, group theory, generalized cohomology theories and multiplicative structures, the theory of iterated loop spaces, Smith-Toda complexes, and topological modular forms.
Invariant Methods in Discrete and Computational Geometry
Invariant, or coordinate-free methods provide a natural framework for many geometric questions. Invariant Methods in Discrete and Computational Geometry provides a basic introduction to several aspects of invariant theory, including the supersymmetric algebra, the Grassmann-Cayler algebra, and Chow forms. It also presents a number of current research papers on invariant theory and its applications to problems in geometry, such as automated theorem proving and computer vision. Audience: Researchers studying mathematics, computers and robotics.
Abelian Group Theory and Related Topics
This volume contains the proceedings of a conference on abelian groups held in August 1993 at Oberwolfach. The conference brought together forty-seven participants from all over the world and from a range of mathematical areas. Experts from model theory, set theory, noncommutative groups, module theory, and computer science discussed problems in their fields that relate to abelian group theory. This book provides a window on the frontier of this active area of research.
Inverse Scattering and Applications
This book presents papers given at a Conference on Inverse Scattering on the Line, held in June 1990 at the University of Massachusetts, Amherst. A wide variety of topics in inverse problems were covered: inverse scattering problems on the line; inverse problems in higher dimensions; inverse conductivity problems; and numerical methods. In addition, problems from statistical physics were covered, including monodromy problems, quantum inverse scattering, and the Bethe ansatz. One of the aims of the conference was to bring together researchers in a variety of areas of inverse problems which have seen intensive activity in recent years. scattering
Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups
This book contains papers presented by speakers at the AMS-IMS-SIAM Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, held at Mount Holyoke College in June 1992. One group of papers deals with one aspect of conformal field theory, namely, vertex operator algebras or superalgebras and their representations. Another group deals with various aspects of quantum groups. Other topics covered include the theory of knots in three-manifolds, symplectic geometry, and tensor products. This book provides an excellent view of some of the latest developments in this growing field of research.
Azumaya Algebras, Actions, and Modules
This volume contains the proceedings of a conference in honor of Goro Azumaya's seventieth birthday, held at Indiana University of Bloomington in May 1990. Professor Azumaya, who has been on the faculty of Indiana University since 1968, has made many important contributions to modern abstract algebra. His introduction and investigation of what have come to be known as Azumaya algebras subsequently stimulated much research on such rings and algebras, as well as applications to geometry and number theory. In addition to honoring Professor Azumaya's contributions, the conference was intended to stimulate interaction among three areas of his research interests; Azumaya algebras, group and Hopf algebra actions, and module theory. Aimed at researchers in algebra, this volume contains contributions by some of the leaders in these areas.
