Commutative Algebra
A.Y. 2025/2026
Learning objectives
The main task is to give an introduction to modern commutative algebra with a special regard to commutative ring theory, arithmetic, homological methods and algebraic geometry.
Expected learning outcomes
Theory and computations of primary decompositions, integral extensions, regular rings & a first step in dimension theory.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
First steps in dimension theory in the sense of Krull and via trascendence theory, examples in dimension 0 and 1, integral extensions, going up theorem, Noether normalization lemma, regular rings, Kahler differentials, finite ètale extensions, covers, introduction to the etale fundamental group
Prerequisites for admission
The contents of the courses Algebra 1, 2, 3 ,4.
Teaching methods
classical lectures
Teaching Resources
Notes of the course (available on Ariel).
Atiyah, MacDonald, "Introduction to Commutative Algebra"
"Galois Theory for schemes", Notes by H. Lenstra, available online.
Atiyah, MacDonald, "Introduction to Commutative Algebra"
"Galois Theory for schemes", Notes by H. Lenstra, available online.
Assessment methods and Criteria
Homeworks, oral exam.
Professor(s)
Reception:
By appointment only, on Thursday 10:30-12:30
Office 2093