Derived Categories and Derived Functors

Sergei I. Gelfand () and Yuri I. Manin
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Sergei I. Gelfand: American Mathematical Society
Yuri I. Manin: MPI für Mathematik

Chapter Chapter III in Methods of Homological Algebra, 1996, pp 139-238 from Springer

Abstract: Abstract Homological algebra was founded by D. Hilbert. He considered, in particular, the following problem. Let $$ \sum\nolimits_{j = 1}^m {{a_{ij}}{x_j} = 0;\;i = 1, \ldots ,n;{a_{ij}}} \in k\left[ {{t_1}, \ldots {t_r}} \right] $$ , be a system of linear homogeneous equations with coefficients lying in the polynomial ring over a field. All polynomial solutions are linear combinations (with polynomial coefficients) of a finite subset of solutions. However, in general there exists no basis of solutions that are linearly independent over k[t 1..., t r]. Linear relations among elements of a generating system of solutions are, in turn, linear combinations of some finite set of relations, and again it might happen that there exists no free system of generators for relations.

Keywords: Exact Sequence; Spectral Sequence; Full Subcategory; Derive Functor; Abelian Category (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-3-662-03220-6_3

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