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- Academic unit or major
- Mathematics
- Instructor(s)
- Kelly Shane
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Thr5-6(H137)
- Group
- -
- Course number
- ZUA.A333
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 3Q
- Syllabus updated
- 2018/9/17
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
Motivated by Weil's beautiful conjectures on zeta functions counting points on varieties over finite fields, étale cohomology is a theory generalising singular cohomology of complex algebraic varieties. In the first half we give an introduction to the classical theory of étale cohomology. In the second half, we will discuss Bhatt-Scholze's pro-étale topology. For more information see: http://www.math.titech.ac.jp/~shanekelly/EtaleCohomology2018-19WS.html
Student learning outcomes
(1) Obtain overall knowledge on basics in étale cohomology
(2) Understand the relationship between étale topology and Galois theory
(3) Attain understanding of possible applications of étale topology
Keywords
Étale cohomology, homological algebra, Galois theory
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 | Introduction | Details will be provided during each class. |
| Class 2 | Commutative Algebra I | Details will be provided during each class. |
| Class 3 | Topology I | Details will be provided during each class. |
| Class 4 | Homological Algebra I | Details will be provided during each class. |
| Class 5 | Functoriality I | Details will be provided during each class. |
| Class 6 | Étale cohomology I | Details will be provided during each class. |
| Class 7 | Étale cohomology II | Details will be provided during each class. |
| Class 8 | Fundamental group I | Details will be provided during each class. |
Textbook(s)
None required
Reference books, course materials, etc.
Milne, James S. "Etale cohomology, volume 33 of Princeton Mathematical Series." (1980).
Assessment criteria and methods
Based on the reports with answers of exercise problems presented in the class.
Related courses
- MTH.A407 ： Advanced topics in Algebra C1
- MTH.A408 ： Advanced topics in Algebra D1
- ZUA.A334 ： Advanced courses in Algebra D
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basic knowledge of scheme theory (e.g., Hartshorne)
Other
Details TBD
