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Author: Amnon Yekutieli
Publisher: Cambridge University Press
Published: 2019-12-19
Total Pages: 621
ISBN-13: 110841933X
DOWNLOAD EBOOK →The first systematic exposition of the theory of derived categories, with key applications in commutative and noncommutative algebra.
Author: Saunders Mac Lane
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 320
ISBN-13: 1475747217
DOWNLOAD EBOOK →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: Fedor Bogomolov
Publisher: Springer Science & Business Media
Published: 2009-11-03
Total Pages: 316
ISBN-13: 0817649344
DOWNLOAD EBOOK →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: Daniel Huybrechts
Publisher: Oxford University Press
Published: 2006-04-20
Total Pages: 316
ISBN-13: 0199296863
DOWNLOAD EBOOK →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: Yuri Tschinkel
Publisher: Springer Science & Business Media
Published: 2010-08-05
Total Pages: 723
ISBN-13: 0817647457
DOWNLOAD EBOOK →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: Masaki Kashiwara
Publisher: Springer Science & Business Media
Published: 2005-12-19
Total Pages: 496
ISBN-13: 3540279504
DOWNLOAD EBOOK →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: Leonid Positselski
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 146
ISBN-13: 0821852965
DOWNLOAD EBOOK →"July 2011, volume 212, number 996 (first of 4 numbers)."
Author: Robert Penner
Publisher: Springer Nature
Published: 2020-04-25
Total Pages: 201
ISBN-13: 3030439968
DOWNLOAD EBOOK →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
Publisher: Cambridge University Press
Published: 2007-01-04
Total Pages: 482
ISBN-13: 9780521680455
DOWNLOAD EBOOK →A handbook of key articles providing both an introduction and reference for newcomers and experts alike.
Author: Steffen König
Publisher: Springer
Published: 2006-11-14
Total Pages: 256
ISBN-13: 3540697489
DOWNLOAD EBOOK →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.
