Notes characterising higher and derived stacks concretely

Details Notes characterising higher and derived stacks concretely Notes characterising higher and derived stacks concretely

2011-05-24

arxiv.org/abs/1105.4853v2

Mathematics

Algebraic Geometry

Only 9 pages long; v2 slightly expanded and typos fixed

Scientific paper

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.

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