nLab
cohomological descent

Context

Locality and descent

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

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.

For a readable introduction see

Closely related is the monadic descent in triangulated context in the sense of page 36-37 in

  • A. L. Rosenberg, Topics in noncommutative algebraic geometry, homological algebra and K-theory, preprint MPIM Bonn 2008-57 pdf
Revised on December 17, 2011 14:33:45 by Urs Schreiber (89.204.137.170)