Derived Algebraic Geometry V: Structured Spaces
Jacob Lurie
TL;DR
This paper develops a comprehensive framework for structured spaces with sheaves, unifying classical schemes, stacks, and their derived counterparts within a broad theoretical setting.
Contribution
It introduces a general theory of structured spaces that encompasses various existing geometric theories and their derived extensions.
Findings
Unified framework for classical and derived geometric spaces
Inclusion of schemes, stacks, and their derived versions
Foundation for further research in structured algebraic geometry
Abstract
In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their derived generalizations.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models