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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Taguchi Yuichiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Thr5-6()
- Group
- -
- Course number
- MTH.A407
- Credits
- 1
- Academic year
- 2021
- Offered quarter
- 3Q
- Syllabus updated
- 2021/3/19
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
In number theory, L-functions are associated with various arithmetic objects. In this course, we explain the interpretation of L-functions based on Galois representations and discuss important results/conjectures on them. This course together with "Advanced Course in Algebra D1" given in 4Q forms one set of contents. Basic materials are dealt with in the first half "C1".
Student learning outcomes
Students are expected to:
- understand fundamental notions and methods in algebraic number theory and Galois representation theory.
- understand the interpretation of L-functions based on Galois representation theory.
Keywords
L-function, Euler product, Galois representation, Frobenius, Hasse-Weil Conjecture
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. There will be some assignments.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Various L-functions | Details will be provided during each class session |
| Class 2 | Preparation from algebraic number theory | Details will be provided during each class session |
| Class 3 | Galois representations | Details will be provided during each class session |
| Class 4 | L-functions revisited | Details will be provided during each class session |
| Class 5 | Weil Conjectures (Part 1) | Details will be provided during each class session |
| Class 6 | Weil Conjectures (Part 2) | Details will be provided during each class session |
| Class 7 | Drinfeld modules and t-motives | Details will be provided during each class session |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to indulge themselves in L-functions and Galois representations.
Textbook(s)
None required.
Reference books, course materials, etc.
None required.
Assessment criteria and methods
Course scores are evaluated by homework assignments (100%). Details will be announced during the course.
Related courses
- Algebra III
- MTH.A408 ： Advanced topics in Algebra D1
- ZUA.A334 ： Advanced courses in Algebra D
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basic knowledge in undergraduate algebra
Other
None in particular.
