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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Honda Nobuhiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri5-6(H119A)
- Group
- -
- Course number
- MTH.B505
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 1Q
- Syllabus updated
- 2017/3/17
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
In this lecture series we basic materials on sheaf theory, cohomology group with sheaf coefficients, and de Rham theorem, and so on. Cohomology group with sheaf coefficients are useful especially in the theory of complex manifolds. The course is followed by MTH.B506.
Student learning outcomes
・to know the concept of sheaf and be familiar with basic examples
・to be able to handle exact sequence of cohomology groups
・to understand the mechanism of the proof of de Rham theorem
Keywords
sheaf, presheaf, cohomology group, exact sequence, deRham theorem, intersection form, Poincare's theorem on intersection forms
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 | sheaves, basic examples, homomorphism of sheaves | Details will be provided during each class session. |
| Class 2 | presheaves, basic examples, relation with sheaves, sheafification | |
| Class 3 | cohomology group with sheaf coefficients | |
| Class 4 | exact sequence of cohomology groups | |
| Class 5 | deRham theorem, double complex | |
| Class 6 | fine sheaf, Leray's theorem, acyclic covering | |
| Class 7 | Poincare's duality on homology groups | |
| Class 8 | dual cell decomposition, deRham group and intersection forms |
Textbook(s)
none
Reference books, course materials, etc.
P. Griffiths, J. Harris, "Principles of Algebraic Geometry", Wiley-Interscience
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.B506 ： Advanced topics in Geometry F1
- MTH.E532 ： Special lectures on advanced topics in Mathematics H
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basic knowledge on geometry (manifolds, differential forms, homology group) is required.
