The theory of local Chern characters used in commutative algebra originated in topology about thirty years ago, and from there was introduced in algebraic geometry. This book describes the theory in an algebraic setting, presenting recent research results and important algebraic applications, some of which come from the author's own work. It concentrates on the background in commutative algebra and homological algebra and describes the relations between these subjects, including extensive discussions of the homological conjectures and of the use of the Frobenius map. It will be particularly useful for graduate students and researchers.
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Editorial Reviews
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"This book will be of enormous value to algebraists who want to gain an understanding of the powerful techniques presented in [F] and how they can be applied to local algebra." Bulletin of the AMS
"The book covers a variety of interesting subjects in commutative algebra and makes an algebraic version of the intersection theory accessible to a wide audience. It contains many new points of view, and the presentation is easy to follow. This is an excellent book." Mathematical Reviews
"The book covers a variety of interesting subjects in commutative algebra and makes an algebraic version of the intersection theory accessible to a wide audience. It contains many new points of view, and the presentation is easy to follow. This is an excellent book." Mathematical Reviews
Book Description
In recent years there have been new developments in the field of commutative algebra which led to proofs of several conjectures which had been open for many years. Many of these proofs rely on techniques from topology and algebraic geometry, making them difficult for students and even researchers specializing in algebra to read. This book describes the mathematical background necessary to prove these results and sets them in their algebraic context.
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Inside This Book
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First Sentence:
The main purpose of this chapter is to define the Chow group of a Noetherian ring and prove several of its basic properties. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
grade conjecture, multiplicativity formula, new intersection theorem, canonical sheaves, finite projective dimension, free subsheaves, mixed multiplicities, locally free quotient, characters commute, homological conjectures, graded prime ideal, free sheaves, locally free subsheaf, minimal free resolution, associated prime ideal, projective map, regular local ring, minimal injective resolution, dualizing complex, modulo rational equivalence, maximal minors, classes commute, free sheaf, divisorial ideals, polynomial whose value Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Acyclicity Lemma, Proof Suppose New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
The main purpose of this chapter is to define the Chow group of a Noetherian ring and prove several of its basic properties. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
grade conjecture, multiplicativity formula, new intersection theorem, canonical sheaves, finite projective dimension, free subsheaves, mixed multiplicities, locally free quotient, characters commute, homological conjectures, graded prime ideal, free sheaves, locally free subsheaf, minimal free resolution, associated prime ideal, projective map, regular local ring, minimal injective resolution, dualizing complex, modulo rational equivalence, maximal minors, classes commute, free sheaf, divisorial ideals, polynomial whose value Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Acyclicity Lemma, Proof Suppose New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 13
books:
See all 13 books this book cites
3
books
cite this book:
- Introduction To Commutative Algebra by Michael Atiyah in Front Matter, and Back Matter
- Intersection Theory, 2nd Edition by William Fulton in Front Matter, and Back Matter
- Determinantal Rings (Lecture Notes in Mathematics, 1327) by Winfried Bruns in Back Matter
- The Algebraic Theory of Modular Systems (Cambridge Mathematical Library) by F. S. Macaulay in Back Matter
- Local Rings (Tracts in Pure & Applied Mathematics) by M. Nagata in Back Matter
See all 13 books this book cites
- Commutative Algebra: Geometric, Homological, Combinatorial and Computational Aspects (Lecture Notes in Pure and Applied Mathematics) by Alberto Corso on page 68
- Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series (Ergebnisse der Mathematik Und Ihrer Grenzgebiete) by R.K. Lazarsfeld in Back Matter
- Local Algebra (Springer Monographs in Mathematics) by Jean-Pierre Serre in Back Matter
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