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- Academic unit or major
- Mathematics
- Instructor(s)
- Somekawa Mutsuro
- Class Format
- Lecture (Livestream)
- Media-enhanced courses
- Day/Period(Room No.)
- Thr5-6(H119A)
- Group
- -
- Course number
- ZUA.A331
- Credits
- 1
- Academic year
- 2022
- Offered quarter
- 1Q
- Syllabus updated
- 2022/3/16
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
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".
Student learning outcomes
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 that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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 |
Out-of-Class Study Time (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.
Assessment criteria and methods
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 (i.e., required knowledge, skills, courses, etc.)
basic undergraduate algebra
