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- Academic unit or major
- Mathematics
- Instructor(s)
- Taguchi Yuichiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Thr5-6(H137)
- Group
- -
- Course number
- ZUA.A331
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 1Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
In this course, we define the zeta functions of Galois representations in the most general setting, and discuss their basic properties and expected properties. As a preparation, we explain basic facts on Galois representations. This course is followed by "Advanced Course in Algebra B" in the second quarter.
Student learning outcomes
To become familiar with basic notions such as Galois representations, zeta functions, etc.
Building upon them, to think what is new yourself.
Keywords
Galois representation, zeta function
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Exercise sessions are integrated into the normal lecture format.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Zeta functions | Details will be provided during each class session |
| Class 2 | Galois representations | Details will be provided during each class session |
| Class 3 | Algebraic number theory | Details will be provided during each class session |
| Class 4 | Motives | |
| Class 5 | Zeta functions of Galois representations | Details will be provided during each class session |
| Class 6 | Taniyama-Shimura Conjecture | Details will be provided during each class session |
| Class 7 | Sato-Tate Conjecture | Details will be provided during each class session |
| Class 8 | Langlands Conjecture | Details will be provided during each class session |
Textbook(s)
None required
Reference books, course materials, etc.
Takeshi Saito, "Fermat Conjecture", Iwanami, 2009
Proceedings of "The arithmetic of l-adic Galois representations and Galois deformations"
http://www.math.sci.osaka-u.ac.jp/~ochiai/ss2009proceeding/ss2009proceeding.html
Proceedings of "Recent developments on Ｒ＝Ｔ"
http://www.kurims.kyoto-u.ac.jp/~gokun/R=T.html
Assessment criteria and methods
By reports. Details will be announced in the course.
Related courses
- ZUA.A332 ： Advanced courses in Algebra B
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None required
