2022 Students Enrolled in or before 2015 School of Science Mathematics
Advanced courses in Algebra A
- Academic unit or major
- Mathematics
- Instructor(s)
- Mutsuro Somekawa
- Class Format
- Lecture (Livestream)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Thu (H119A)
- Class
- -
- Course Code
- ZUA.A331
- Number of credits
- 100
- Course offered
- 2022
- Offered quarter
- 1Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
The theory of étale cohomology is given the impotant tools to number theory, arithmetic geometry, representation theory, etc. Galois cohomologies are étale cohomologies of fields. In this course, we give an introduction to the theory of Galois ohomology. After reviewing Galois theory for fields, we explain the definition and basic properties of Galois cohomology.
This course is followed by "Advanced Topics in Algebra B".
Course description and aims
The goal of this course is to understand:
(1) the definition of Galois cohomology,
(2) how to calculate low-dimensional Galois cohomologies.
Keywords
homological algebra, Galois theory, Galois cohomology
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Introduction | Details will be provided during each class session |
| Class 2 | infinite dimensional Galois theory | Details will be provided during each class session |
| Class 3 | homological algebra | Details will be provided during each class session |
| Class 4 | cohomology of groups | Details will be provided during each class session |
| Class 5 | Galois cohomology (1) | Details will be provided during each class session |
| Class 6 | Galois cohomology (2) | Details will be provided during each class session |
| Class 7 | Application: local field | Details will be provided during each class session |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 30 minutes preparing for class and another 30 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None required.
Reference books, course materials, etc.
Course materials are provided during class.
Evaluation methods and criteria
Course scores are evaluated by homework assignments. Details will be announced during the course.
Related courses
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
- MTH.A331 ： Algebra III
Prerequisites
basic undergraduate algebra