Welcome to MATH 520! This course will be an introduction to techniques in commutative and homological algebra that one encounters in algebraic geometry, number theory and topology. Topics will include Hilbert's Nullstellensatz, primary decomposition, dimension theory, Ext, Tor, Koszul complexes, etc.
Prerequisites: MATH 516 and MATH 517, or a year of graduate algebra.
Time and Venue: MWF 11:00--11:50 in SEO 636 (NOTE VENUE CHANGE!).
Lecturer: Izzet Coskun
Office: SEO 423
Required text: The course will mostly follow D. Eisenbud, Commutative Algebra with a view towards Algebraic Geometry. Other recommended texts are Atiyah and MacDonald, Introduction to Commutative Algebra and Matsumura, Commutative Algebra.
Grading: There will be problem sets. These problem sets will account for your entire grade. To receive an A, you must turn in at least 100 problem solutions from Eisenbud, Matsumura or Atiyah-MacDonald by December 5.
Homework:
Week I: Read Chapters 1 and 2 of Eisenbud.
Suggested problems: 1.1, 1.3, 1.7, 1.9, 1.10, 1.11, 1.13, 1.14, 1.15, 1.18, 1.19, 1.24
Suggested problems: 2.4, 2.6, 2.10, 2.13, 2.14, 2.17, 2.19, 2.22, 2.23
Week II: Read Chapters 3 and 4 of Eisenbud
Suggested problems: 3.1, 3.2, 3.3, 3.4, 3.6, 3.7, 3.8, 3.14, 3.15
Suggested problems: 4.1, 4.3, 4.4, 4.5, 4.6, 4.7, 4.11, 4.12, 4.14, 4.15, 4.16, 4.17, 4.18, 4.19, 4.20, 4.26, 4.27, 4.28, 4.29, 4.30, 4.31
Week III: Read Chapters 4 and 5 of Eisenbud
Suggested problems: 5.4, 5.5, 5.6, 5.7, 5.8
Week IV: Read Chapters 6 and 7 of Eisenbud
Suggested problems: 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.8, 6.9, 6.11, 6.12
Suggested problems: 7.1, 7.2, 7.3, 7.4, 7.6, 7.7, 7.8, 7.9, 7.10,
Week V: Read Chapter 8 of Eisenbud
Suggested Problems 7.11, 7.12, 7.13, 7.14, 7.15-7.18
Week VI: Read Chapters 9, 10 of Eisenbud
Suggested Problems: 9.1-9.6
Suggested Problems: 10.1-10.4, 10.6, 10.11-10.14
Week VII: Read Chapters 11, 12, 13 of Eisenbud
Suggested Problems: 11.1-11.6, 11.7, 11.9, 11.11, 11.12, 11.13
Suggested Problems: 12.1-12.5, 12.6-12.12
Week VIII: Read Chapters 13, 14 of Eisebud
Suggested Problems: 13.1, 13.6, 13.7, 13.8, 13.9-13.12, 13.13, 13.14, 13.15, 13.16
Suggested Problems: 14.1, 14.2, 14.3, 14.4, 14.5, 14.6-14.8
Week IX: Read chapters 16, 17 of Eisenbud
Suggested problems: 16.1-16.3, 16.5-16.7, 16.8, 16.11, 16.13, 16.14, 16.15, 16.16, 16.17
Suggested problems: 17.1-17.10, 17.11, 17.12, 17.14, 17.16, 17.17, 17.18, 17.19, 17.20, 17.21
Week X: Read Chapters 17, 18 of Eisenbud