2021 Advanced courses in Algebra C

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Academic unit or major
Mathematics
Instructor(s)
Taguchi Yuichiro 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Thr5-6(H137)  
Group
-
Course number
ZUA.A333
Credits
1
Academic year
2021
Offered quarter
3Q
Syllabus updated
2021/3/19
Lecture notes updated
-
Language used
English
Access Index

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

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