Notes characterising higher and derived stacks concretely
Algebraic Geometry
2024-06-27 v4 Algebraic Topology
Abstract
This is an informal summary of the main concepts in arXiv:0905.4044, based on notes of various seminars. It gives constructions of higher and derived stacks without recourse to the extensive theory developed by Toen, Vezzosi and Lurie. Explicitly, higher stacks are described in terms of simplicial diagrams of affine schemes, which are analogous to atlases for manifolds. We also describe quasi-coherent sheaves and complexes on such objects.
Keywords
Cite
@article{arxiv.1105.4853,
title = {Notes characterising higher and derived stacks concretely},
author = {J. P. Pridham},
journal= {arXiv preprint arXiv:1105.4853},
year = {2024}
}
Comments
Only 11 pages long; v2 slightly expanded and typos fixed; v3 refs updated, Theorems 3.3, 5.11 and 5.17 added; v4 corrected typo in Definition 5.10