Lecture 1 - Course outline and Fundamentals
Lecture 2 - Ideals and Varieties
Lecture 3 - Dimension of Varieties
Lecture 4 - Projective varieties
Lecture 5 - Morphisms and rational functions
Lecture 6 - Local rings
Lecture 7 - Rational maps and Birationality
Lecture 8 - Tangent space and Singularities
Lecture 9 - Resolution of singularities
Lecture 10 - Discrete valuation rings
Lecture 11 - Existence of nonsingular model
Lecture 12 - Nonsingular curves
Lecture 13 - Divisor on Curves
Lecture 14 - Riemann-Roch Spaces - I
Lecture 15 - Riemann-Roch Spaces - II
Lecture 16 - Divisor Class Group
Lecture 17 - Genus of a curve
Lecture 18 - Riemann-Roch and Adeles
Lecture 19 - Differentials and Riemann-Roch
Lecture 20 - Canonical divisor and proof of Riemann-Roch
Lecture 21 - Jacobian of a curve
Lecture 22 - Zeta function of curves
Lecture 23 - Functional equation and point counting
Lecture 24 - Riemann hypothesis for curves
Lecture 25 - Proof of RH for curves: Galois covers
Lecture 26 - Proof of RH for curves II: Multilinear algebra
Lecture 27 - Cohomological interpretation of zeta function
