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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Kelly Shane
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Thr5-6(H137)
- Group
- -
- Course number
- MTH.A404
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 4Q
- Syllabus updated
- 2018/10/19
- Lecture notes updated
- -
- Language used
- English
- Access Index
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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 | The pro-étale topology | Details will be provided during each class session |
| Class 2 | Commutative algebra II | Details will be provided during each class session |
| Class 3 | Homological algebra II | Details will be provided during each class session |
| Class 4 | Topology II | Details will be provided during each class session |
| Class 5 | Functoriality II | Details will be provided during each class session |
| Class 6 | Functoriality III | Details will be provided during each class session |
| Class 7 | Functoriality IV | Details will be provided during each class session |
| Class 8 | Fundamental group II | Details will be provided during each class session |
Textbook(s)
None required
Reference books, course materials, etc.
Milne, James S. "Etale cohomology, volume 33 of Princeton Mathematical Series." (1980).
Bhatt, Bhargav, and Peter Scholze. "The pro-\'etale topology for schemes." arXiv preprint arXiv:1309.1198 (2013).
Assessment criteria and methods
Course scores are evaluated by homework assignments. Details will be announced during the course.
Related courses
- MTH.A403 ： Advanced topics in Algebra C
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basic knowledge of scheme theory (e.g., Hartshorne)
