Algebraic Geometry II
Schemes as functors, Grothendieck topologies. Groupoids, fibered categories, pseudofunctors, 2-categories. Algebraic spaces, algebraic (DM) stacks. Internal groupoids, presentations, global quotient stacks. Statement of Artin's theorem, application to moduli stacks. Infinitesimal criteria for smoothness and etaleness, tangent and obstruction spaces, deformation theory. Derived category, cotangent complex.
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