Special courses on advanced topics in Mathematics H

Academic unit or major

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

ZUA.E342

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

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.