Rigid Complexes via DG Algebras

Details Rigid Complexes via DG Algebras Rigid Complexes via DG Algebras

2006-03-31

arxiv.org/abs/math/0603733v3

Mathematics

Commutative Algebra

38 pages, AMSLaTeX, xypic figures. Final version, minor changes, to appear in Tran. AMS

Scientific paper

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square Sq_{B/A} M, which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism \rho : M \iso Sq_{B/A} M then the pair (M,\rho) is called a rigid complex over B relative to A (there are some finiteness conditions). There is an obvious notion of rigid morphism between rigid complexes. We establish several properties of rigid complexes, including their uniqueness, existence (under some extra hypothesis), and formation of pullbacks f^{\flat}(M,\rho) (resp. f^{\sharp}(M,\rho)) along a finite (resp. essentially smooth) ring homomorphism f^* : B \to C. In a subsequent paper we consider rigid dualizing complexes over commutative rings, building on the results of the present paper. The project culminates in a third paper, where we give a comprehensive version of Grothendieck duality for schemes. The idea of rigid complexes originates in noncommutative algebraic geometry, and is due to Van den Bergh.

Affiliated with

Also associated with

No associations

Rating

Rigid Complexes via DG Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rigid Complexes via DG Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rigid Complexes via DG Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-332559