Commutative algebra and algebraic geometry

Syllabus

Algebraic curves

• Preliminaries LN: 1, 2.
• Projective curves LN: 3, 4.
• Some local-global methods LN: 5, 6.
• On the canonical class LN: 7, 8.

Dimension theory

• Noetherian rings LN: 9, 10.
• Trascendence bases LN: 11, 12.
• Integral ring extensions LN: 13, 14.
• Hilbert's Nullstellensatz LN: 15, 16.

Valuation rings

• One dimensional Noetherian domains LN: 17, 18.
• Dedekind domains LN: 19, 20.
• Some local rings LN: 21, 22.
• Norm, trace,and discriminant LN: 23, 24.

Regular functions

• The Zariski topology
• On the basic open sets
• The sheaf of regular functions
• Ringed spaces

Facultad de Ciencias
Bernal Diaz del Castillo 340
28045 Colima
Mexico