| Academic Year |
2025Year |
School/Graduate School |
Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program |
| Lecture Code |
WSA70004 |
Subject Classification |
Specialized Education |
| Subject Name |
数学特別講義（正標数の代数幾何） |
Subject Name
（Katakana） |
スウガクトクベツコウギ |
Subject Name in
English |
Special Lectures in Mathematics |
| Instructor |
To be announced.,SHIMADA ICHIROU |
Instructor
(Katakana) |
タントウキョウインミテイ,シマダ イチロウ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, Second Semester, 3Term |
| Days, Periods, and Classrooms |
(3T) Inte |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| Blackboard |
| Credits |
1.0 |
Class Hours/Week |
|
Language of Instruction |
B
:
Japanese／English |
| Course Level |
5
:
Graduate Basic
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
Algebraic surfaces, Quotient singularities, Jacobson-Galois theory |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Class Objectives
/Class Outline |
In the theory of algebraic varieties, many peculiar phenomena occur when the characteristic of the base field is positive.
Behind these phenomena, there is always a "purely inseparable extension of a field”.
When a purely inseparable field extension is involved, Galois theory in field extensions cannot be applied, but it is possible to develop analogous theories using tools such as derivations and group schemes. This will greatly advance research into varieties and singularities specific to positive characteristic.
Through these lectures, I will introduce the world specific to positive characteristic.
|
| Class Schedule |
1. Purely inseparable field extensions, Galois and Jacobson-Bourbaki correspondence
2. Algebraic surfaces in positive characteristics
3. Finite group scheme actions and their quotients
4. Further topics, unification of wild group and group scheme actions |
Text/Reference
Books,etc. |
R. Hartshorne, Algebraic Geometry, GTM 52, Springer.
宮西正宜、代数幾何学、裳華房.
N. Jacobson, Lectures in Algebra, Vol. III, GTM 32, Springer.
Miyanishi-Ito, Algebraic Surfaces in Positive Characteristics, World Scientific.
Further textbooks and papers are indicated in the lecture.
|
PC or AV used in
Class,etc. |
|
| (More Details) |
|
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
Basic theory of algebra |
| Requirements |
Students need good knowledge on algebra, especially, basics on group theory, ring theory and Galois theory.
Students should understand abstract theories through a variety of examples.
|
| Grading Method |
Evaluation is based on submitted answers to the problems given in the lecture. |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |