The Derived Category of Sheaves of Commutative DG Rings (Preview)
  In this short paper we outline (mostly without proofs) our new approach to the derived category of sheaves of commutative DG rings. The proofs will appear in a subsequent paper.   Among other things, we explain how to form the derived intersection of two closed subschemes inside a given algebraic scheme X, without recourse to simplicial or higher homotopical methods, and without any global assumptions on X. 
Amnon Yekutieli
math.AG math.AT math.KT