▶Japanese
Post to SNS
- Home
- > School of Science
- > Graduate major in Mathematics
- > Advanced topics in Algebra E
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Kato Fumiharu
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon5-6(H116)
- Group
- -
- Course number
- MTH.A501
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 1Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
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.
Student learning outcomes
(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 that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Introduction: Tate curve | Details will be provided during each class session |
| Class 2 | Affinoid algebras (1) | Details will be provided during each class session |
| Class 3 | Affinoid algebras (2) | Details will be provided during each class session |
| Class 4 | Maximal spectrum (1) | Details will be provided during each class session |
| Class 5 | Maximal spectrum (1) | Details will be provided during each class session |
| Class 6 | Affinoid subdomains | Details will be provided during each class session |
| Class 7 | Affinoid spaces (1) | Details will be provided during each class session |
| Class 8 | Affinoid spaces (2) | Details will be provided during each class session |
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)
Assessment criteria and methods
Course scores are evaluated by homework assignments. Details will be announced during the course.
Related courses
- MTH.A502 ： Advanced topics in Algebra F
- MTH.C301 ： Complex Analysis I
- MTH.C302 ： Complex Analysis II
- MTH.A201 ： Introduction to Algebra I
- MTH.A202 ： Introduction to Algebra II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
basic undergraduate algebra and complex analysis
