The Derived Category of Sheaves of Commutative DG Rings (Preview)
Amnon Yekutieli
TL;DR
This paper introduces a novel approach to the derived category of sheaves of commutative DG rings, enabling derived intersections of subschemes without complex homotopical methods or global assumptions.
Contribution
It presents a new framework for derived categories of sheaves of commutative DG rings, simplifying intersection constructions without advanced homotopical tools.
Findings
Provides a method for derived intersection without simplicial or homotopical methods
Applicable to algebraic schemes without global assumptions
Outlines the theoretical foundation for future detailed proofs
Abstract
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory