Notes on Grothendieck topologies, fibered categories and descent theory

Abstract

This is an introduction to Grothendieck's descent theory, with some stress on the general machinery of fibered categories and stacks.

114 pages. I have corrected a finite, but extremely high, number of errors that have been pointed out to me by various readers. These were mostly typos, but a couple were substantial

References in corpus (1)

• Introduction to the language of stacks and gerbes

Cited by in corpus (36)

• Construction of Hilbert and Quot Schemes
• Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
• On p-adic lattices and Grassmannians
• Log differentiable spaces and manifolds with corners
• The Grothendieck Construction and Gradings for Enriched Categories
• The homotopy groups of the spectrum Tmf
• A Self-Dual Integral Form of the Moonshine Module
• Grothendieck topologies and ideal closure operations
• Principal actions of stacky Lie groupoids
• Algebraic colimit calculations in homotopy theory using fibred and cofibred categories
• The moduli space of curves and its invariants
• Higgs bundles, abelian gerbes and cameral data
• The categorical Weil representation
• From fibered symmetric bimonoidal categories to symmetric spectra
• Higher rank flag sheaves on Surfaces and Vafa-Witten invariants
• Geometric Class Field Theory
• Localization of ringed spaces
• Cobordism bicycles of vector bundles
• Modular equivariant formality
• A Comparison of the functors of points of Supermanifolds
• Manifolds, Structures Categorically
• Logarithmic stacks and minimality
• Unified Functorial Signal Representation I: From Grothendieck fibration to Base structured categories
• Commutative character sheaves and geometric types for supercuspidal representations
• On Conjugates and Adjoint Descent
• Zigzag normalisation for associative $n$-categories
• Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu)
• Families of Supermanifolds: Splitting Types and Obstruction Maps
• Birational Geometry of moduli spaces of pointed curves
• Deformations of Lie algebras of vector fields arising from families of schemes
• Categorical Results in the Theory of Two-Crossed Modules of Commutative Algebras
• Some equivariant constructions in noncommutative algebraic geometry
• Parametrized K-Theory
• The L-group of a covering group
• Consequences of the existence of exceptional collections in arithmetic and rationality
• Analytic moduli spaces of simple sheaves on families of integral curves