Slides:

- Lecture 1: Hilbert Nullstellensatz (August 13).
- Lecture 2: Hilbert Nullstellensatz and categories (August 17).
- Lecture 3: Strong Nullstellensatz (August 24).
- Lecture 4: Smooth manifolds (August 27).
- Lecture 5: Noetherian rings and irreducible affine varieties (August 31)
- Lecture 6: Representations of finite groups (September 3).
- Lecture 7: Tensor product of R-modules (September 10).
- Lecture 8: Tensor product of rings and fibered product (September 14).
- Lecture 9: Finite-dimensional algebras over a field (September 17).
- Lecture 10: Primitive element theorem (September 21).
- Lecture 11: Normal varieties (September 24).
- Lecture 12: Normalization (September 28).
- Lecture 13: Nakayama's lemmma (October 1).
- Lecture 14: Finite quotients and branched covers (October 5).
- Lecture 15: Noether normalization lemma (October 8).
- Lecture 16: Covering maos and Galois categories (October 15).
- Lecture 17: Discriminant (October 19).
- Lecture 18: Dimension (October 22).
- Lecture 19: Projective varieties (October 26).
- Lecture 20: Sheaves and algebraic varieties (October 29).
- Lecture 21: Veronese map (November 5).
- Lecture 22: Segre map and quadric hypersurfaces (November 9).
- Lecture 23: Images of projective varieties are projective (November 12).
- Lecture 24: Hilbert polynomial (November 16).
- Lecture 25: Constructible sets (November 19).

- Home assignment 1: Zorn lemma (August 17).
- Home assignment 2: Applications of Axiom of Choice (August 17).
- Home assignment 3: Euclidean rings (August 24).
- Class assignment 4: Exercises in set theory (September 6). Results.
- Home assignment 5: Hermitian spaces (September 10)
- Home assignment 6: Tensor product (September 14)
- Class assignment 7: Exercises in divisibility (September 27)
- Home assignment 8: Representation of finite groups (September 28)
- Class assignment 9: Exercises in divisibility (2) (October 4) Results.
- Class assignment 10: Regular functions and Nullstellensatz (October 11) Results.
- Class assignment 11: Representations of finite groups (October 18) Results.
- Class assignment 12: Noetherian rings (October 25) Results.
- Class assignment 13: Rational functions (November 1) Results.
- Total score for all assignments.

- Exam problems
- Personal problem sets, obtained randomly with this program.

Misha VerbitskyIMPA |