Misha Verbitsky

Instituto Nacional de Matemática Pura e Aplicada

Commutative Algebra

17:00-18:30, Mondays, Fridays - Sala 236

Slides:

• Lecture 1: Algebraic sets and Hilbert Nullstellensatz (March 16).
• Lecture 2: Strong Nullstellensatz and equivalence of categories (March 20).
• Lecture 3: Noetherian rings and irreducible affine varieties (March 23)
• Lecture 4: Irreducible varieties: smoothness and primary decomposition (March 27)
• Lecture 5: The ring of G-invariants (March 30)
• Lecture 6: Tensor product (April 6)
• Lecture 7: Tensor products of rings and products of varieties (April 10)
• Lecture 8: Artinian rings (April 13)
• Lecture 9: Some Galois theory (April 17)
• Lecture 10: Normal varieties (April 20)
• Lecture 11: Nakayama's lemma (April 24)
• Lecture 12: Normalization (May 4)
• Lecture 13: Krull dimension and algebraic dimension (May 8)
• Lecture 14: Fractional ideals (May 18)
• Lecture 15: Discrete valuation rings (May 22)
• Lecture 16: Dedekind rings (May 25)
• Lecture 17: Smooth points in algebraic varieties (May 29)
• Lecture 18: Hilbert polynomial (June 1)

Handouts

• Handout 1: Remedial set theory (March 16). Results
• Handout 2: Noetherian rings (March 23) Results
• Handout 3: Tensor product (March 30). Results
• Handout 4: Artinian rings (April 13). Results
• Handout 5: Factorial rings (April 20)
• Handout 6: Divisibility in rings of integers (April 27)
• Handout 7: Representations of finite groups (May 4)
• Handout 8: Equivalence of categories (May 18)
• Handout 9: p-adic numbers (May 26)
• Handout 10: Poincare series (June 1)

Misha Verbitsky IMPA