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André-Quillen homology

Idea

André-Quillen cohomology is the cochain cohomology of the derived Kähler differentials, hence of the cotangent complex (for the moment see there for more).

Related concepts

• topological André-Quillen homology

References

The orginal work comes from two sources, the work of Michel André and that of Dan Quillen:

• Michel André, Méthode simpliciale en algèbre homologique et algèbre commutative, Springer Lecture Notes in Mathematics, Vol 32, 1967.

• Michel André, Homologie des algèbres commutatives Grundlehren der mathematischen Wissenschaften, Band 206. Springer. 1974

and then

• D. G. Quillen, 1970, On the (co-)homology of commutative rings, in Proc. Symp. on Categorical Algebra, 65–87, American Math. Soc.