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- Tags: - #study-guides - Refs: - Quick overview: https://math.uchicago.edu/~may/REU2013/REUPapers/Fung.pdf#page=3 - Links: - scheme

scheme definitions

• O_X module
  • locally free sheaf
• ideal sheaf
• direct image
• inverse image
• affine scheme
• Common assumptions:
  • Noetherian scheme
  • integral scheme
  • separated scheme
  • regular in codimension one
• regular scheme
• Cohen-Macaulay
• open subscheme
• closed immersion
• closed subscheme
• locally of finite type
• quasiseparated morphism
• proper
  • universally closed morphism
  • separated morphism
  • finite type
• projective (schemes)
• quasiprojective scheme
• flat morphism
• Proj
• sheaf associated to a module
• quasicoherent
• invertible sheaf
• twisting sheaf
• prime divisor
• Weil divisor