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 Panoramas et Synthèses 2004; 132 pp; softcover Number: 16 ISBN-10: 2-85629-159-7 ISBN-13: 978-2-85629-159-7 List Price: US$36 Member Price: US$28.80 Order Code: PASY/16 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. Pirashvili present A. Scorichenko's understanding of the stable $$K$$-theory of rings as functor homology. The book is suitable for graduate students and researchers interested in algebra and algebraic geometry. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in algebra and algebraic geometry. Table of Contents Introduction to functor homology Lectures on the cohomology of finite group schemes Algèbre de Steenrod, modules instables et foncteurs polynomiaux L'algèbre de Steenrod en topologie Stable $$K$$-theory is bifunctor homology (after A. Scorichenko) Index of notation Index Index terminologique