2020 Advanced topics in Algebra D

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Kato Fumiharu 
Course component(s)
Lecture
Mode of instruction
ZOOM
Day/Period(Room No.)
Thr5-6(Zoom)  
Group
-
Course number
MTH.A404
Credits
1
Academic year
2020
Offered quarter
4Q
Syllabus updated
2020/9/18
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 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

Out-of-Class Study Time (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)

Assessment criteria and methods

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 (i.e., required knowledge, skills, courses, etc.)

Basic knowledge of scheme theory (e.g., Hartshorne)

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