- Jarod Alper’s course: https://sites.math.washington.edu/~jarod/math582C.html
- Martin Olsson’s, Algebraic spaces and stacks.
- What is a stack?, by Dan Edidin.
- Equivariant geometry and the cohomology of the moduli space of curves, by Dan Edidin.
- Notes on the construction of the moduli space of curves, by Dan Edidin.
- Stacks for Everybody, by Barbara Fantechi.
- Picard groups of moduli problems, by David Mumford, and Daniel Litt’s exposition thereof (parts one and two).
- Notes on Grothendieck topologies, fibered categories and descent theory, by Angelo Vistoli (lovely comprehensive reference).
- More notes
Definitions
- What is the blowup of a scheme? The blowdown of a scheme?
- What is a site?
- What is a topos?
- What is the Hilbert scheme?
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Topologies:
- What is the etale topology?
- What is the fppf topology?
- What is the etale site?
- What is an algebraic space?
- What is Faithfully flat descent?
- What is a torsor?
- What is the Amtisur complex?
- What does it mean to have a closed subcategory?
- What does it mean for a subcategory to be local on the base? local on the domain?
- What does it mean to have a stable subcategory?
- What is an etale equivalence relation?
- What is a locally closed substack?
- What is an orbifold?
- What is a smooth stack?
Results
- What is the local criterion for flatness?
- What is the infinitesimal criterion for flatness?
Problems
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- For schemes with structure sheaves taking values in R-algebras, An/−:=Γ((−);O−)×n:Schop→Alg/RX↦Γ(X;OX)\carptpowernf↦f∗, which is represented by SpecZ[x0,⋯,xn].
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- x↦x=[x1,⋯,xn] where not all of the xi are zero.
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- R=k[x][(x(x−1))−1]