2023 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Special lectures on advanced topics in Mathematics H
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Naoki Imai / Tadashi Ochiai
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Intensive (本館2階201数学系セミナー室)
- Class
- -
- Course Code
- MTH.E532
- Number of credits
- 200
- Course offered
- 2023
- Offered quarter
- 4Q
- Syllabus updated
- Jul 8, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Recently, Fargues-Scholze formulated a geometrization of the local Langlands correspondences using the idea of the geometric Langlands correspondence. In this lecture, I will explain the formulation and necessary concepts. If time permits, I will also discuss related results.
Course description and aims
Aim is to learn and get used to various concepts which appear in the formulation of the geometrization of the local Langlands correspondence.
Keywords
local Langlands correspondence, perfectoid space and diamond, Fargues-Fontaine curve, Geometric Satake equivalence
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | The following topics will be covered: -- Local Langlands correspondence -- Perfectoid space and diamond -- Fargues-Fontaine curve -- Geometric Satake equivalence -- Geometrization of the local Langlands correspondence | 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 materials.
Textbook(s)
None required
Reference books, course materials, etc.
Laurent Fargues, Peter Scholze, Geometrization of the local Langlands correspondence
https://arxiv.org/abs/2102.13459
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