HX205700 Special Lectures in Mathematics(Periods of algebraic curves and regulators)

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Science

Lecture Code HX205700 Subject Classification Specialized Education

Subject Name 数学特別講義（代数曲線の周期とレギュレーター）

Subject Name
（Katakana）スウガクトクベツコウギ（ダイスウキョクセンノシュウキトレギュレーター）

Subject Name in
English Special Lectures in Mathematics(Periods of algebraic curves and regulators)

Instructor To be announced.,TAKAHASHI NOBUYOSHI

Instructor
(Katakana) タントウキョウインミテイ,タカハシ　ノブヨシ

Campus Higashi-Hiroshima Semester/Term 4th-Year, Second Semester, Second Semester

Days, Periods, and Classrooms (2nd) Inte

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

Blackboard, class materials will be distributed

Credits 1.0 Class Hours/Week 　 Language of Instruction J : Japanese

Course Level 4 : Undergraduate Advanced

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords

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 this lecture, you will learn basic properties of algebraic curves over number fields and Riemann surfaces. As applications, you will learn the definitions of number-theoretic quantities called periods and regulators, important in Beilinson Conjecture, their basic properties and how to calculate them. The goal is to understand the statement of Beilinson Conjecture and to be able to do numerical calculations in concrete examples.

Class Schedule Algebraic curves and Riemann surfaces, I
Algebraic curves and Riemann surfaces, II
Periods of algebraic curves and Riemann surfaces
Definition of regulators and their basic properties
Beilinson Conjecture

A report assignment is planned. Problems will be distributed in the middle of the lectures.

Text/Reference
Books,etc. (1) Lang, Serge: Introduction to algebraic and abelian functions. Second edition. Graduate Texts in Mathematics, 89. Springer-Verlag, New York-Berlin, 1982. ix+169 pp.

(2) Ramakrishnan, Dinakar: Regulators, algebraic cycles, and values of L-functions. Algebraic K-theory and algebraic number theory (Honolulu, HI, 1987), 183--310, Contemp. Math., 83, Amer. Math. Soc., Providence, RI, 1989.

PC or AV used in
Class,etc.

(More Details)

Learning techniques to be incorporated

Suggestions on
Preparation and
Review Review the basics of complex analysis and theories of groups, rings and fields.

Requirements

Grading Method Based on reports.

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.

Academic Year	2026Year	School/Graduate School	School of Science
Lecture Code	HX205700	Subject Classification	Specialized Education
Subject Name	数学特別講義（代数曲線の周期とレギュレーター）
Subject Name （Katakana）	スウガクトクベツコウギ（ダイスウキョクセンノシュウキトレギュレーター）
Subject Name in English	Special Lectures in Mathematics(Periods of algebraic curves and regulators)
Instructor	To be announced.,TAKAHASHI NOBUYOSHI
Instructor (Katakana)	タントウキョウインミテイ,タカハシ　ノブヨシ
Campus	Higashi-Hiroshima	Semester/Term	4th-Year, Second Semester, Second Semester
Days, Periods, and Classrooms	(2nd) Inte
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face
Blackboard, class materials will be distributed
Credits	1.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	4 : Undergraduate Advanced
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords
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 this lecture, you will learn basic properties of algebraic curves over number fields and Riemann surfaces. As applications, you will learn the definitions of number-theoretic quantities called periods and regulators, important in Beilinson Conjecture, their basic properties and how to calculate them. The goal is to understand the statement of Beilinson Conjecture and to be able to do numerical calculations in concrete examples.
Class Schedule	Algebraic curves and Riemann surfaces, I Algebraic curves and Riemann surfaces, II Periods of algebraic curves and Riemann surfaces Definition of regulators and their basic properties Beilinson Conjecture A report assignment is planned. Problems will be distributed in the middle of the lectures.
Text/Reference Books,etc.	(1) Lang, Serge: Introduction to algebraic and abelian functions. Second edition. Graduate Texts in Mathematics, 89. Springer-Verlag, New York-Berlin, 1982. ix+169 pp. (2) Ramakrishnan, Dinakar: Regulators, algebraic cycles, and values of L-functions. Algebraic K-theory and algebraic number theory (Honolulu, HI, 1987), 183--310, Contemp. Math., 83, Amer. Math. Soc., Providence, RI, 1989.
PC or AV used in Class,etc.
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	Review the basics of complex analysis and theories of groups, rings and fields.
Requirements
Grading Method	Based on reports.
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.

Back to syllabus main page