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Rational representations, the Steenrod algebra and functor homology. (English) Zbl 1061.18011
Panoramas et Synthèses 16. Paris: Société Mathématique de France (ISBN 2-85629-159-7/pbk). xxi, 132 p. (2003).

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Publisher’s description: The book presents aspects of homological algebra in functor categories, with emphasis on polynomial functors between vector spaces over a finite field. With these foundations in place, the book presents applications to representation theory, algebraic topology and K-theory. As these applications reveal, functor categories offer powerful computational techniques and theoretical insights. T. Pirashvili sets the stage with a discussion of foundations. E. Friedlander then presents applications to the rational representations of general linear groups. L. Schwartz emphasizes the relation of functor categories to the Steenrod algebra. Finally, V. Franjou and T. Pirashivili present A. Scorichenko’s understanding of the stable K-theory of rings as functor homology.
Indexed articles:
Pirashvili, Teimuraz, Introduction to functor homology, 1-26 [Zbl 1072.18009]
Friedlander, Eric M., Lectures on the cohomology of finite group schemes, 27-53 [Zbl 1069.14050]
Schwartz, Lionel, The Steenrod algebra, unstable modules and polynomial functors, 55-100 [Zbl 1060.55007]
The Steenrod algebra in topology, 101-106 [Zbl 1060.55005]
Franjou, Vincent; Pirashvili, Teimuraz, Stable \(K\)-theory is bifunctor homology (after A. Scorichenko), 107-126 [Zbl 1063.19002]
Franjou, Vincent, Introduction, xiii-xxi [Zbl 1058.18001]

18G60 Other (co)homology theories (MSC2010)