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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Ochiai Tadashi
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive (本館2階201数学系セミナー室)
- Group
- -
- Course number
- MTH.E532
- Credits
- 2
- Academic year
- 2023
- Offered quarter
- 4Q
- Syllabus updated
- 2023/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
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.
Student learning outcomes
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 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.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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. |
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
Assessment criteria and methods
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 (i.e., required knowledge, skills, courses, etc.)
Basic knowledge on algebra is expected
