Commutative_Algebra_2019

Commutative algebra (fall 2019)

lecturer: Anton Khoroshkin,

Literature

• • Атья, Макдональд. Введение в коммутативную алгебру. Мир 1972.

• M.Atiyah, "Introduction to commutative algebra." Vol. 361. Westview press, 1994.

• M.Reid, "Undergraduate commutative algebra." Vol. 29. Cambridge University Press, 1995.

  • G.Kemper. "A course in commutative algebra." Vol. 256. Springer Science Business Media, 2010.

  • D.Eisenbud. "Commutative Algebra: With a View Toward Algebraic Geometry." New York, NY: Springer-Verlag, 1999

  • Д.Айзенбад. "Коммутативная алгебра с прицелом на алгебраическую геометрию"

General information

Your final grade is a weighted sum of

-- Final written exam (50%), Exam info!

-- Written midterm (30%),

-- Small tests during seminars (30%).

5.06 и 12.06 семинаров не будет

Сonduct sheet // Кондуит

Preliminary program

Exercises

• 1. Rings, ideals and modules

  2. Prime ideals

1. Noetherian rings

2. Nakayama's lemma; UFD

3. Rings and modules of fractions

4. More on localization

5. Integral dependence

6. Going up/down

7. Noether normalization

8. Hilbert's Nullstellensatz

9. Spectrum

10. Constructible subsets

11. Dimension

12. Artinian rings and Dedekind domains

    1. Hilbert series

13. Primary decomposition

14. All up to date seminars in one file

Schedule and titles of lectures/seminars

- Lectures will be held on Thursdays room 108, 14.00 - 15.30,Two identical seminars will be on - Wednesdays (12.00 -- 13.20) and Thursday (15.30 -- 16.50).

• • 17.01 Rings and Ideals (Кольца и идеалы),

  • 24.01 Noetherian rings (Нётеровы кольца),

  • 31.01 Unique factorization (Факториальные кольца),

  • 7.02 Rings of fractions (Кольца частных)

  • 14.02 Localization functor (Функтор локализации)

  • 21.02 Integral dependence (Целая зависимость)

  • 28.02 Going up theorem (Теорема о подъеме)

  • 7.03 Going down (Теорема о спуске)

  • 14.03 Noether normalization theorem (Лемма Нётер о нормализации)

  • 21.03 Seminar instead of lecture because of the sickness of the lecturer

  • 27.03 Семинара в среду не будет в связи с весенней сессией.

  • 28.03 Ring spectrum

  • 4.04 Midterm

  • 11.04 Max spectrum

  • 18.04 Dimension theory

  • 25.04 Artinian rings

  • 26.04 (Friday) 2pm auditorium 108 -- one more attempt of Midterm

• may vacation (1.05 -- 10.05)

  • 16.05 Discrete valuation rings, Dedekind domains

  • 23.05 Hilbert series

• 30.05 Final exam (for those who has to be graded before May 31'st)

• 5.06 и 12.06 семинаров не будет (приходите на семинар в четверг)

  • 6.06 Primary decomposition

  • 13.06 Completions. Exam consultation during the seminar

• 18.06 19.06. Final exam (for everybody, who is not yet graded)!