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
(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
Étale cohomology, homological algebra, Galois theory
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course
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 |
None required
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).
Course scores are evaluated by homework assignments. Details will be announced during the course.
Basic knowledge of scheme theory (e.g., Hartshorne)