Lectures On The Theory Of Pure Motives PDF Download
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| Author | : Jacob P. Murre |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 163 |
| Release | : 2013-04-11 |
| Genre | : Mathematics |
| ISBN | : 082189434X |
Download Lectures on the Theory of Pure Motives Book in PDF, ePub and Kindle
The theory of motives was created by Grothendieck in the 1960s as he searched for a universal cohomology theory for algebraic varieties. The theory of pure motives is well established as far as the construction is concerned. Pure motives are expected to h
| Author | : Gonçalo Tabuada |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 127 |
| Release | : 2015-09-21 |
| Genre | : Mathematics |
| ISBN | : 1470423979 |
Download Noncommutative Motives Book in PDF, ePub and Kindle
The theory of motives began in the early 1960s when Grothendieck envisioned the existence of a "universal cohomology theory of algebraic varieties". The theory of noncommutative motives is more recent. It began in the 1980s when the Moscow school (Beilinson, Bondal, Kapranov, Manin, and others) began the study of algebraic varieties via their derived categories of coherent sheaves, and continued in the 2000s when Kontsevich conjectured the existence of a "universal invariant of noncommutative algebraic varieties". This book, prefaced by Yuri I. Manin, gives a rigorous overview of some of the main advances in the theory of noncommutative motives. It is divided into three main parts. The first part, which is of independent interest, is devoted to the study of DG categories from a homotopical viewpoint. The second part, written with an emphasis on examples and applications, covers the theory of noncommutative pure motives, noncommutative standard conjectures, noncommutative motivic Galois groups, and also the relations between these notions and their commutative counterparts. The last part is devoted to the theory of noncommutative mixed motives. The rigorous formalization of this latter theory requires the language of Grothendieck derivators, which, for the reader's convenience, is revised in a brief appendix.
| Author | : Pavel Mnev |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 192 |
| Release | : 2019-08-20 |
| Genre | : Algebras, Linear |
| ISBN | : 1470452715 |
Download Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications Book in PDF, ePub and Kindle
This book originated from lecture notes for the course given by the author at the University of Notre Dame in the fall of 2016. The aim of the book is to give an introduction to the perturbative path integral for gauge theories (in particular, topological field theories) in Batalin–Vilkovisky formalism and to some of its applications. The book is oriented toward a graduate mathematical audience and does not require any prior physics background. To elucidate the picture, the exposition is mostly focused on finite-dimensional models for gauge systems and path integrals, while giving comments on what has to be amended in the infinite-dimensional case relevant to local field theory. Motivating examples discussed in the book include Alexandrov–Kontsevich–Schwarz–Zaboronsky sigma models, the perturbative expansion for Chern–Simons invariants of 3-manifolds given in terms of integrals over configurations of points on the manifold, the BF theory on cellular decompositions of manifolds, and Kontsevich's deformation quantization formula.
| Author | : Mark L. Green |
| Publisher | : Springer |
| Total Pages | : 281 |
| Release | : 2004-09-02 |
| Genre | : Mathematics |
| ISBN | : 3540490469 |
Download Algebraic Cycles and Hodge Theory Book in PDF, ePub and Kindle
The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.
| Author | : Corrado De Concini |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 153 |
| Release | : 2017-11-16 |
| Genre | : Invariants |
| ISBN | : 147044187X |
Download The Invariant Theory of Matrices Book in PDF, ePub and Kindle
This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving (1) the first fundamental theorem that describes a set of generators in the ring of invariants, and (2) the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.
| Author | : Thomas Dedieu |
| Publisher | : Springer Nature |
| Total Pages | : 421 |
| Release | : 2023-04-14 |
| Genre | : Mathematics |
| ISBN | : 303111938X |
Download The Art of Doing Algebraic Geometry Book in PDF, ePub and Kindle
This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.
| Author | : Raymond Cheng |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 219 |
| Release | : 2020-05-28 |
| Genre | : Education |
| ISBN | : 1470455935 |
Download Function Theory and ℓp Spaces Book in PDF, ePub and Kindle
The classical ℓp sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces ℓpA of analytic functions whose Taylor coefficients belong to ℓp. Relations between the Banach space ℓp and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of ℓpA and a discussion of the Wiener algebra ℓ1A. Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.
| Author | : Federico Binda |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 267 |
| Release | : 2020-03-09 |
| Genre | : Education |
| ISBN | : 147044898X |
Download Motivic Homotopy Theory and Refined Enumerative Geometry Book in PDF, ePub and Kindle
This volume contains the proceedings of the Workshop on Motivic Homotopy Theory and Refined Enumerative Geometry, held from May 14–18, 2018, at the Universität Duisburg-Essen, Essen, Germany. It constitutes an accessible yet swift introduction to a new and active area within algebraic geometry, which connects well with classical intersection theory. Combining both lecture notes aimed at the graduate student level and research articles pointing towards the manifold promising applications of this refined approach, it broadly covers refined enumerative algebraic geometry.
| Author | : Robert Steinberg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 160 |
| Release | : 2016-12-22 |
| Genre | : Algebraic geometry -- Algebraic groups -- Algebraic groups |
| ISBN | : 147043105X |
Download Robert Steinberg Book in PDF, ePub and Kindle
Robert Steinberg's Lectures on Chevalley Groups were delivered and written during the author's sabbatical visit to Yale University in the 1967–1968 academic year. The work presents the status of the theory of Chevalley groups as it was in the mid-1960s. Much of this material was instrumental in many areas of mathematics, in particular in the theory of algebraic groups and in the subsequent classification of finite groups. This posthumous edition incorporates additions and corrections prepared by the author during his retirement, including a new introductory chapter. A bibliography and editorial notes have also been added.
| Author | : Carlo Mazza |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 240 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9780821838471 |
Download Lecture Notes on Motivic Cohomology Book in PDF, ePub and Kindle
The notion of a motive is an elusive one, like its namesake "the motif" of Cezanne's impressionist method of painting. Its existence was first suggested by Grothendieck in 1964 as the underlying structure behind the myriad cohomology theories in Algebraic Geometry. We now know that there is a triangulated theory of motives, discovered by Vladimir Voevodsky, which suffices for the development of a satisfactory Motivic Cohomology theory. However, the existence of motives themselves remains conjectural. This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, etale cohomology, and Chow groups. The book is divided into lectures, grouped in six parts. The first part presents the definition of Motivic Cohomology, based upon the notion of presheaves with transfers. Some elementary comparison theorems are given in this part. The theory of (etale, Nisnevich, and Zariski) sheaves with transfers is developed in parts two, three, and six, respectively. The theoretical core of the book is the fourth part, presenting the triangulated category of motives. Finally, the comparison with higher Chow groups is developed in part five. The lecture notes format is designed for the book to be read by an advanced graduate student or an expert in a related field. The lectures roughly correspond to one-hour lectures given by Voevodsky during the course he gave at the Institute for Advanced Study in Princeton on this subject in 1999-2000. In addition, many of the original proofs have been simplified and improved so that this book will also be a useful tool for research mathematicians. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
