KOSZUL DUALITY AND CODERIVED CATEGORIES (AFTER K. LEFEVRE)
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].
Bernhard Keller, le 4 octobre, 2003.