2020 Students Enrolled in or before 2015 School of Science Mathematics
Advanced courses in Algebra D
- Academic unit or major
- Mathematics
- Instructor(s)
- Fumiharu Kato
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Thu (H137)
- Class
- -
- Course Code
- ZUA.A334
- Number of credits
- 100
- Course offered
- 2020
- Offered quarter
- 4Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
Rigid Geometry is a modern framework of geometry, established by Tate and Raynaud in an attempt to obtain analytic geometry over non-archimedean fields such as p-adic fields, and is nowadays becoming more and more important in several areas of mathematics, not only in algebraic and arithmetic geometries. The aim of this lecture is to cover overall basics of rigid geometry.
Course description and aims
(1) Obtain overall knowledge on basics in rigid geometry
(2) Understand the relationship between rigid geometry and formal geometry
(3) Attain deep understanding of possible applications of rigid geometry
Keywords
Rigid geometry, Formal geometry, Non-archimedean uniformization
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Rigid analytic spaces (1) | Details will be provided during each class session |
| Class 2 | Rigid analytic spaces (2) | Details will be provided during each class session |
| Class 3 | Relation with formal geometry (1) | Details will be provided during each class session |
| Class 4 | Relation with formal geometry (2) | Details will be provided during each class session |
| Class 5 | GAGA (1) | Details will be provided during each class session |
| Class 6 | GAGA (2) | Details will be provided during each class session |
| Class 7 | Applications (1) | Details will be provided during each class session |
| Class 8 | Applications (2) | 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 textbooks and other course material.
Textbook(s)
None required
Reference books, course materials, etc.
S. Bosch "Lectures on Formal and Rigid Geometry", Lecture Notes in Mathematics, Springer Verlag (978-3-319-04416-3)
K. Fujiwara, F. Kato "Foundations of Rigid Geometry I", EMS Monographs in Mathematics, European Mathematical Society (978-3-03719-135-4)
Evaluation methods and criteria
Course scores are evaluated by homework assignments. Details will be announced during the course.
Related courses
- MTH.A403 ： Advanced topics in Algebra C
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
Prerequisites
Basic knowledge of scheme theory (e.g., Hartshorne)