KOSZUL DUALITY AND CODERIVED CATEGORIES (AFTER K. LEFEVRE)

Bernhard Keller

This is a brief report on a part of Chapter 2 of K. Lefèvre's thesis. We sketch a framework for Koszul duality [Beilinson-Ginzburg-Soergel, 1996] where the Koszul dual algebra is replaced by a coalgebra. This allows us to free ourselves from many assumptions (for example finiteness assumptions) and leads to clean statements about equivalences between the derived category and a suitably defined coderived category. These results are related to work by G. Floystad. Our approach is based on classical developments in topology (cf. [Husemoller-Moore-Stasheff, 1974] or [Moore, 1970]) and inspired by [Hinich, 2001].

http://www.math.jussieu.fr/~keller/publ/kdcabs.html

Bernhard Keller, le 4 octobre, 2003.
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