cohomology

# Contents

## Idea

The theory of cohomological descent deals with the question if the derived analogue of the (co)monadic comparison functor is fully faithful (or more rarely an equivalence of categories) when formulated at the level of total derived functors and derived categories, and usually taken with respect to hypercovers.

## References

The notion has been introduced in

• Pierre Deligne, Théorie de Hodge. III, Inst. Hautes Études Sci. Publ. Math. 44 (1974), 5–77.

A summary is also in

• Donu Arapura, Building mixed Hodge structures, in: The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), 13–32, CRM Proc. Lecture Notes, 24, Amer. Math. Soc., Providence, RI, 2000.