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.
(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
Rigid geometry, Formal geometry, Non-archimedean uniformization
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
Standard lecture course
|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 (2)||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|
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.
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)
Based on the reports with answers of exercise problems presented in the class.
Basic knowledge of scheme theory (e.g., Hartshorne)