The Derived Category of Sheaves of Commutative DG Rings (Preview) Academic Article uri icon

abstract

  • A . In this short paper we outline (mostly without proofs) our new ap- proach 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 sim- plicial or higher homotopical methods, and without any global assumptions on X … 1. Pseudo-Free Sheaves of Commutative Graded Rings … 2. Pseudo-Semi-Free Sheaves of Commutative DG Rings … 3. Relative Quasi-Homotopies and the Derived Category … 4. Left Derived Tensor Products of Sheaves of DG Rings … In the theory of DG schemes – a simplified variant of derived algebraic geometry – it is important to have a suitable way to resolve a sheaf of rings by a flat sheaf of DG rings. A typical problem is this: X is a scheme, and Y1,Y2 … (Of course, it is enough to resolve only one of the …

publication date

  • January 1, 2016

published in