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 | 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. |
None required
Milne, James S. "Etale cohomology, volume 33 of Princeton Mathematical Series." (1980).
Based on the reports with answers of exercise problems presented in the class.
Basic knowledge of scheme theory (e.g., Hartshorne)
Details TBD