Emmanuel Kowalski: Catalogue data in Autumn Semester 2021

Name Prof. Dr. Emmanuel Kowalski
FieldMathematics
Address
Professur für Mathematik
ETH Zürich, HG G 64.1
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 34 41
E-mailemmanuel.kowalski@math.ethz.ch
URLhttp://www.math.ethz.ch/~kowalski
DepartmentMathematics
RelationshipFull Professor

NumberTitleECTSHoursLecturers
401-3132-00LCommutative Algebra Information 10 credits4V + 1UE. Kowalski
AbstractThis course provides an introduction to commutative algebra. It serves in particular as a foundation for modern algebraic geometry.
ObjectiveThe 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
LiteraturePrimary 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 / NoticePrerequisites: Algebra I/II (or a similar introduction to the basic concepts of ring theory, including field theory).
401-5110-00LNumber Theory Seminar Information 0 credits1KÖ. Imamoglu, E. Kowalski, R. Pink, G. Wüstholz
AbstractResearch colloquium
Objective