Emmanuel Kowalski: Catalogue data in Autumn Semester 2021 |
Name | Prof. Dr. Emmanuel Kowalski |
Field | Mathematics |
Address | Professur für Mathematik ETH Zürich, HG G 64.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
Telephone | +41 44 632 34 41 |
emmanuel.kowalski@math.ethz.ch | |
URL | http://www.math.ethz.ch/~kowalski |
Department | Mathematics |
Relationship | Full Professor |
Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|
401-3132-00L | Commutative Algebra | 10 credits | 4V + 1U | E. Kowalski | |
Abstract | This course provides an introduction to commutative algebra. It serves in particular as a foundation for modern algebraic geometry. | ||||
Objective | The topics presented in the course will include: * Basics facts about rings, ideals and modules * Constructions of rings: quotients, polynomial rings, localization * Noetherian rings and modules * The tensor product of modules over commutative rings and its applications * Krull dimension * Integral extensions and the Cohen-Seidenberg theorems * Finitely generated algebrais over fields, including the Noether Normalization Theorem and the Nullstellensatz * Primary decomposition * Discrete valuation rings and some applications | ||||
Literature | Primary Reference: "(Mostly) Commutative Algebra", by A. Chambert-Loir; Springer 2021, available on the author's web page. Secondary References: 1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969) 2. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995) 3. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989) 4. "Commutative Algebra" by N. Bourbaki | ||||
Prerequisites / Notice | Prerequisites: Algebra I/II (or a similar introduction to the basic concepts of ring theory, including field theory). | ||||
401-5110-00L | Number Theory Seminar | 0 credits | 1K | Ö. Imamoglu, E. Kowalski, R. Pink, G. Wüstholz | |
Abstract | Research colloquium | ||||
Objective |