Derived Category Methods in Commutative Algebra by Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm
- Derived Category Methods in Commutative Algebra
- Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm
- Page: 1119
- Format: pdf, ePub, mobi, fb2
- ISBN: 9783031774522
- Publisher: Springer Nature Switzerland
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Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendieck’s Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to expand. This book guides readers familiar with rings and modules through the construction of the associated derived category and its triangulated functors. In this context, it develops theories of categorical equivalences for subcategories and homological invariants of objects. The second half of the book focuses on applications to commutative Noetherian rings. The book can be used as a text for graduate courses, both introductory and advanced, and is intended to serve as a reference for researchers in commutative algebra and related fields. To accommodate readers new to homological algebra, it offers a significantly higher level of detail than most existing texts on the subject.
On the derived category of a finite-dimensional algebra.
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I read in the book Methods of homological algebra of Gelfand and Manin that the derived category of an abelian category A is never abelian. Now
Derived Category Methods in Commutative Algebra
Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of
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Note. Our first theorem is an application of the second one: Corso, Huneke, Katz, Vasconcelos: I is pd-test.
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Manin: Methods of homological algebra, Springer-Verlag (1996). [12] D. Happel: On the derived category of a finite dimensional algebra. Comment. Math. Helv
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There are many formal similarities between homological algebra and algebraic topology. The Dold-Kan correspondence, for example, provides a dictionary.
Derived Category Methods in Commutative Algebra
Zusammenfassung: Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a
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