Stacks and Moduli

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?
  • 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

      • For schemes with structure sheaves taking values in R-algebras, An/:=Γ(();O)×n:SchopAlg/RXΓ(X;OX)\carptpowernff, which is represented by SpecZ[x0,,xn].
      • xx=[x1,,xn] where not all of the xi are zero.
    • R=k[x][(x(x1))1]
🗓️ Timeline
Links to this page