学部・大学院区分
Undergraduate / Graduate		多・博前
時間割コード
Registration Code		3211091
科目区分
Course Category		Ａ類Ⅱ（専門科目）
Category A-2
科目名　【日本語】
Course Title		数理科学特論V
科目名　【英語】
Course Title		Topics in Mathematical Science V
コースナンバリングコード
Course Numbering Code
担当教員　【日本語】
Instructor		DARPOE Erik Olof ○
担当教員　【英語】
Instructor		DARPOE Erik Olof ○
単位数
Credits		2
開講期・開講時間帯
Term / Day / Period		秋 木曜日 ３時限
Fall Thu 3
授業形態
Course style
学科・専攻
Department / Program
多元数理科学研究科
必修・選択
Required / Selected


授業の目的　【日本語】
Goals of the Course(JPN)
授業の目的　【英語】
Goals of the Course
To give an introduction to the modular representation theory of finite groups and self-injective algebras, with focus on homological algebra aspects.
到達目標　【日本語】
Objectives of the Course(JPN))
到達目標　【英語】
Objectives of the Course
At the end of this course, students should have
- an understanding of the main concepts and ideas in the area covered by the course;
- capacity to apply results from the course to solve mathematical problems;
- a thorough understanding of the concept of a mathematical proof;
- capacity to apply the theory to prove new results within the scope of the course.
授業の内容や構成
Course Content / Plan
Elements of module theory, Marschke's theorem, projective modules, tensor products and duality, Frobenius reciprocity, cohomology, the stable module category, triangulated categories, support varieties.
履修条件
Course Prerequisites
General undergraduate mathematics.
Rudimentary knowledge of modern algebra will be assumed. This includes, in particular, basic group theory and the definitions and basic properties of rings and modules.
関連する科目
Related Courses
None
成績評価の方法と基準
Course Evaluation Method and Criteria
Homework assignments and possible oral examination.
教科書・テキスト
Textbook
None
参考書
Reference Book
[1] J. L. Alperin: Local representation theory, Cambridge University Press, Cambridge 1986.
[2] J. F. Carlson: Modules and group algebras, Birhäuser Verlag, Basel, 1996.
[3] A. Zimmermann: Representation theory: a homological algebra point of view. Springer, Cham, 2014.

The course material will be drawn mostly from [1] and [2].
課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours)
Homework assignments to be completed outside of class hours.
Additionally, it is recommended to revise the content of the previous lecture(s) in advance of each class.
注意事項
Notice for Students
Prospective students, who are not present in Nagoya, are requested to contact the instructor before the course starts.
他学科聴講の可否
Propriety of Other department student's attendance
他学科聴講の条件
Conditions of Other department student's attendance
レベル
Level
2
キーワード
Keyword
履修の際のアドバイス
Advice
授業開講形態等
Lecture format, etc.
Face-to-face lectures.
遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class)
Accommodations will be made for students who are not able to attend the lectures in person. Such students are requested to contact the instructor in advance.