2022 Students Enrolled in or before 2015 School of Science Mathematics
Advanced courses in Algebra B
- Academic unit or major
- Mathematics
- Instructor(s)
- Mutsuro Somekawa
- Class Format
- Lecture (Livestream)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Thu (H1104)
- Class
- -
- Course Code
- ZUA.A332
- Number of credits
- 100
- Course offered
- 2022
- Offered quarter
- 2Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
This course is the continuation of "Advanced topics in Algebra A".
The theory of étale cohomology is given the important tools to number theory, arithmetic geometry, representation theory, etc. In this course, we give an introduction to the theory of étale cohomology. We discuss the sheaf theory on Grothendieck topology, and explain the definition and properties of étale cohomology.
Course description and aims
The goal of this course is to understand:
(1) the definition of étale cohomology,
(2) the relationship between étale cohomologies, Galois cohomologies and Zariski cohomologies,
(3) how to calculate low-dimensional étale cohomologies
Keywords
Grothendieck topology, Zariski cohomology, étale 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 | abelian category | Details will be provided during each class session |
| Class 2 | Zariski cohomology | Details will be provided during each class session |
| Class 3 | Grothendieck topology | Details will be provided during each class session |
| Class 4 | étale morphism | Details will be provided during each class session |
| Class 5 | étale cohomology (1) | Details will be provided during each class session |
| Class 6 | étale cohomology (2) | Details will be provided during each class session |
| Class 7 | application | 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