Slides:

- Lecture 1: Algebraic sets and Hilbert Nullstellensatz (January 3).
- Lecture 2: Categories and Hilbert Nullstellensatz (January 6).
- Lecture 3: Strong Nullstellensatz (January 7).
- Lecture 4: Noetherian rings (January 10).
- Lecture 5: Primary decomposition (January 13).
- Lecture 6: The ring of $G$-invariants is finitely generated (January 14).
- Lecture 7: Tensor product of $R$-modules (January 17).
- Lecture 8: Tensor product of rings (January 21).
- Lecture 9: Yoneda lemma and the fibered product (January 24).
- Lecture 10: Tensor product of field extensions (January 27).
- Lecture 11: Primitive element theorem (January 28).
- Lecture 12: Normal varieties (January 31).
- Lecture 13: Gauss Lemma and normalization (February 3).
- Lecture 14: Nakayama lemma (February 4).
- Lecture 15: Finite quotient and branched covers (February 7).
- Lecture 16: Noether normalization lemma (February 10).
- Lecture 17: Krull dimension and algebraic dimension (February 11).
- Lecture 18: Discrete valuation rings (February 14).
- Lecture 19: Discrete valuation rings (2) (February 17).
- Lecture 20: Dedekind rings (February 18).
- Lecture 21: Smooth points in complex varieties (February 21).
- Lecture 22: Hilbert polynomials (February 24).
- Lecture 23: Regular rings and smooth varieties (February 25).

Other materials

- Assignment 1: Zorn lemma (January 6)
- Assignment 2: Applications of Axiom of Choice (January 6)
- Assignment 3: Noetherian rings (January 10)
- Assignment 4: Tensor product (January 17)
- Assignment 5: Factorial rings (January 27)
- Assignment 6: Limits and colimits (January 28)
- Assignment 7: Yoneda lemma (February 3)
- Assignment 8: Exercises in divisibility (February 7)

- Exam problems.
- Personal problem sets, obtained randomly with this program.
- Final results (pending).

Misha VerbitskyIMPA |