2025 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Special lectures on current topics in Mathematics B
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Shuji Saito / Yuri Yatagawa
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- MTH.E632
- Number of credits
- 200
- Course offered
- 2025
- Offered quarter
- 3Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
The aim of the lecture is to explain theory of reciprocity sheaves and its application to ramification theory. The content of the lectures contain:
1. A foundation of theory of reciprocity sheaves.
2. The definition of the motific ramification filtrations for reciprocity sheaves. Its connection with ramification of l-adic sheaves of rank one and irregularities of integrable connections on line bundles.
3. The Zariski-Nagata theorem for motific ramification filtrations.
4. The abbes-Saito theory for motific ramification filtrations and their characteristic forms.
Course description and aims
To understand theory of reciprocity sheaves and its application to ramification theory.
Keywords
Reciprocity sheaves, Ramification theory
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The course will be conducted in the usual lecture format. Reports will be assigned as necessary.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | 1. A foundation of theory of reciprocity sheaves. 2. Motific ramification filtrations on reciprocity sheaves I. 3. Motific ramification filtrations on reciprocity sheaves II. 4. The Zariski-Nagata theorem for motific ramification filtrations. 5. The abbes-Saito theory for motific ramification filtrations and their characteristic forms. | Details will be provided during each class session |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to course material.
Textbook(s)
None.
Reference books, course materials, etc.
None in particular.
Evaluation methods and criteria
Assignments (100%)
Related courses
- MTH.A401 ： Advanced topics in Algebra A
- MTH.A402 ： Advanced topics in Algebra B
- MTH.A501 ： Advanced topics in Algebra E
- MTH.A502 ： Advanced topics in Algebra F
Prerequisites
Basic knowledge on algebra is expected.