**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
- Zariski topology on affine schemes
- 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

- 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