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(Usual) affine schemes
Topics in Non commutative algebraic geometry and congruent zeta functions (Part II). Review of commutative (usual) affine schemes.
Yoshifumi Tsuchimoto
...I used to eat there. Really good noodles.
Neo, ca.1999
(Usual) affine schemes
Spectrums of a commutative ring
ring homomorphism and spectrum
localization of a commutative ring
Existence of a point
Zariski topology on affine schemes
compactness
closed subsets
sheaves
A convention.
presheaves
sheaves
Benefit of being a sheaf.
homomorphisms of (pre)sheaves
example of presheaves and sheafification
sheafification of a sheaf
stalk of a presheaf
kernels, cokernels, etc. on sheaves of modules
general localization of a commutative ring
general localization of modules
local rings
inverse images of sheaves
inverse image of a sheaf
Definition of schemes
tensor products and inverse image of sheaves
tensor products of modules over an algebra
universality of tensor products
additional structures on tensor products
tensor products and localizations
tensor products of sheaves of modules
sheaves associated to modules
direct image of a sheaf
Affine schemes and rings: equivalence of categories
Bibliography
About this document ...
2007-12-11
