2021 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Algebra C1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Yuichiro Taguchi
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Thu
- Class
- -
- Course Code
- MTH.A407
- Number of credits
- 100
- Course offered
- 2021
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
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".
Course description and aims
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
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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 |
Study advice (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.
Evaluation methods and criteria
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
Basic knowledge in undergraduate algebra
Other
None in particular.