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Author : Amnon Yekutieli
Publisher : Cambridge University Press
Page : 621 pages
File Size : 49,8 Mb
Release : 2019-12-19
Category : Mathematics
ISBN : 9781108419338
The first systematic exposition of the theory of derived categories, with key applications in commutative and noncommutative algebra.
Author : Matthew Ballard,Charles Doran,David Favero,Eric Sharpe
Publisher : Springer
Page : 260 pages
File Size : 41,9 Mb
Release : 2018-08-21
Category : Mathematics
ISBN : 9783319916262
This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike. These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math. Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions.
Author : Fedor Bogomolov,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 52,6 Mb
Release : 2009-11-03
Category : Mathematics
ISBN : 9780817649340
Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov
Author : Leonid Positselski
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 50,7 Mb
Release : 2011
Category : Comodules
ISBN : 9780821852965
"July 2011, volume 212, number 996 (first of 4 numbers)."
Author : Masaki Kashiwara,Pierre Schapira
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 48,6 Mb
Release : 2005-12-19
Category : Mathematics
ISBN : 9783540279501
Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.
Author : Annette Huber
Publisher : Springer
Page : 216 pages
File Size : 52,8 Mb
Release : 2006-11-17
Category : Mathematics
ISBN : 9783540492740
The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. The monograph describes the approach to motives via their well-defined realizations. This includes a review of several known cohomology theories. A new absolute cohomology is introduced and studied. The book assumes knowledge of the standard cohomological techniques in algebraic geometry as well as K-theory. So the monograph is primarily intended for researchers. Advanced graduate students can use it as a guide to the literature.
Author : Daniel Huybrechts
Publisher : Oxford University Press on Demand
Page : 316 pages
File Size : 49,5 Mb
Release : 2006-04-20
Category : Mathematics
ISBN : 9780199296866
This work is based on a course given at the Institut de Mathematiques de Jussieu, on the derived category of coherent sheaves on a smooth projective variety. It is aimed at students with a basic knowledge of algebraic geometry and contains full proofs and exercises that aid the reader.
Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 54,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475747218
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
Author : Robert Penner
Publisher : Springer Nature
Page : 201 pages
File Size : 51,8 Mb
Release : 2020-04-25
Category : Mathematics
ISBN : 9783030439965
These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980. He had just received the Fields Medal for his work on these topics among others and was funny and playful with a confident humility from the start. These are not meant to be polished lecture notes, rather, things are presented as did Quillen reflected in the hand-written notes, resisting any temptation to change or add notation, details or elaborations. Indeed, the text is faithful to Quillen's own exposition, even respecting the {\sl board-like presentation} of formulae, diagrams and proofs, omitting numbering theorems in favor of names and so on. This is meant to be Quillen on Quillen as it happened forty years ago, an informal text for a second-semester graduate student on topology, category theory and K-theory, a potential preface to studying Quillen's own landmark papers and an informal glimpse of his great mind. The intellectual pace of the lectures, namely fast and lively, is Quillen himself, and part of the point here is to capture some of this intimacy. To be sure, much has happened since then from this categorical perspective started by Grothendieck, and Misha Kapranov has contributed an Afterword in order to make it more useful to current students.
Author : Lidia Angeleri Hügel,Dieter Happel,Henning Krause
Publisher : Cambridge University Press
Page : 482 pages
File Size : 50,9 Mb
Release : 2007-01-04
Category : Mathematics
ISBN : 052168045X
A handbook of key articles providing both an introduction and reference for newcomers and experts alike.
Author : Yuri Tschinkel,Yuri Zarhin
Publisher : Springer Science & Business Media
Page : 723 pages
File Size : 47,8 Mb
Release : 2010-08-05
Category : Mathematics
ISBN : 9780817647452
EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.
Author : Steffen König,Alexander Zimmermann
Publisher : Springer
Page : 256 pages
File Size : 54,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540697480
A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.
Author : Anonim
Publisher : Academic Press
Page : 334 pages
File Size : 50,8 Mb
Release : 1991-12-02
Category : Psychology
ISBN : 0080863787
Psychology of Learning and Motivation
Author : Dennis Gaitsgory,Nick Rozenblyum
Publisher : American Mathematical Society
Page : 533 pages
File Size : 42,7 Mb
Release : 2019-12-31
Category : Mathematics
ISBN : 9781470452841
Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a “renormalization” of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of $infty$-categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the $mathrm{(}infty, 2mathrm{)}$-category of correspondences needed for the second part. The category of correspondences, via the theory developed in the third part, provides a general framework for Grothendieck's six-functor formalism. The appendix provides the necessary background on $mathrm{(}infty, 2mathrm{)}$-categories needed for the third part.
Author : Masaki Kashiwara,Pierre Schapira
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 48,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662026618
Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.