2024 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Algebra E
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Yuri Yatagawa
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Mon
- Class
- -
- Course Code
- MTH.A501
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
Intersection theory is a fundamental theory in algebraic geometry originating from the number of solutions to systems of simultaneous equations, and it serves as a basis for theories such as the theory of motives, which has been rapidly developing in recent years. This lecture aims to study particularly fundamental concepts within intersection theory.
Course description and aims
(1) Obtain overall knowledge on basics in intersection theory and become proficient in applying them freely
(2) Attain deep understanding of possible applications of intersection theory
Keywords
Intersection theory, algebraic cycles, Chow groups, Segre classes, Chern classes
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Review of schemes | Details will be provided during each class session |
| Class 2 | Algebraic cycle | Details will be provided during each class session |
| Class 3 | Proper push-forward/ flat pull-back | Details will be provided during each class session |
| Class 4 | Divisors | Details will be provided during each class session |
| Class 5 | Intersection products (1) | Details will be provided during each class session |
| Class 6 | Chern classes (1) | Details will be provided during each class session |
| Class 7 | Gysin homomorphism (1) | Details will be provided during each class session |
Study advice (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.
W. Fulton, "Intersection Theory, Second Edition, Springer.
S. Saito and K. Sato, "Algebraic cycles and Etale cohomologies", Maruzen (Japanese).
Evaluation methods and criteria
Course scores are evaluated by homework assignments. Details will be announced during the course.
Related courses
- MTH.A502 ： Advanced topics in Algebra F
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
Prerequisites
A basic knowledge of scheme theory at the level of Hartshorne's book is desirable.
Other
None in particular.