Homological Questions in Local Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Homological Questions in Local Algebra write by Jan R. Strooker. This book was released on 1990-09-06. Homological Questions in Local Algebra available in PDF, EPUB and Kindle. This book presents an account of several conjectures arising in commutative algebra from the pioneering work of Serre and Auslander-Buchsbaum. The approach is via Hochster's 'Big Cohen-Macaulay modules', though the complementary view point of Peskine-Szpiro and Roberts, who study the homology of certain complexes, is not neglected. Various refinements of Hochster's construction, obtained in collaboration with Bartijn, are included. A special feature is a long chapter written by Van den Dries which explains how a certain type of result can be 'lifted' from prime characteristic to characteristic zero. Though this is primarily a research monograph, it does provide introductions to most of the topics treated. Non-experts may therefore find it an appealing guide into an active area of algebra.
An Introduction to Homological Algebra
An Introduction to Homological Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Homological Algebra write by Charles A. Weibel. This book was released on 1995-10-27. An Introduction to Homological Algebra available in PDF, EPUB and Kindle. The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.
Local Fields
Local Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Local Fields write by Jean-Pierre Serre. This book was released on 2013-06-29. Local Fields available in PDF, EPUB and Kindle. The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.
Introduction to Categories, Homological Algebra and Sheaf Cohomology
Introduction to Categories, Homological Algebra and Sheaf Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Categories, Homological Algebra and Sheaf Cohomology write by J. R. Strooker. This book was released on 2009-01-11. Introduction to Categories, Homological Algebra and Sheaf Cohomology available in PDF, EPUB and Kindle. Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields. This textbook provides an introduction to these methods, describing their elements and illustrating them by examples.
Local Algebra
Local Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Local Algebra write by Jean-Pierre Serre. This book was released on 2012-12-06. Local Algebra available in PDF, EPUB and Kindle. This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.
