Étale Cohomology Learning Seminar
This is the syllabus of UIUC étale cohomology learning seminar in summer and fall 2024. A list of discussed topics (subject to changes) can be found here.
Time: 12 pm on Monday in the fall semester. 8 pm CST on Mondays and Fridays in May and June.
Location: Altgeld Hall 141; unless otherwise, which would be English Building 307. on Zoom.
Main References: Milne’s Étale Cohomology, Lectures on Étale Cohomology and Fu’s Étale Cohomology Theory.
Schedule:
| Date | Speaker | Topic |
|---|---|---|
| May 20 | Jiantong Liu | Descent Theory |
| May 24 | Haoran Yin | Étale Topology and Étale Morphisms |
| May 27 | Levi Poon | Henselian Rings, Grothendieck Topology and Sites |
| May 31 | William Chen | Étale Fundamental Group |
| June 3 | Juhan Kim | Sheaves over Étale Topology |
| June 7 | Dinglong Wang | Category of Étale Sheaves |
| June 10 | Ea E Thompson | Direct and Inverse Image of Sheaves |
| June 14 | Jiantong Liu | Étale Cohomology |
| June 21 | Juhan Kim | Čech Cohomology |
| Comparison of Topologies | ||
| June 24 | Haoran Yin | Principal Homogeneous Spaces |
| June 28 | Levi Poon | Constructible Sheaves |
| September 9 | Haoran Yin | Cohomology of Curves |
| September 16 | Juhan Kim | Cohomological Dimension |
| September 23 | Jiantong Liu | Proper Base-change Theorem |
| September 30 | Levi Poon | Higher Direct Image |
| Cohomology with Compact Support | ||
| October 7 | Haoran Yin | Generic Base-change Theorem and Generic Local Acyclicity |
| Finiteness Theorem | ||
| October 14 | Juhan Kim | Smooth Base-change Theorem |
| October 28 | Jiantong Liu | Leray-Serre Spectral Sequence |
| Purity Theorem and Gysin Sequence | ||
| November 18 | Haoran Yin | Künneth Isomorphism |
| Cycles and Chern Classes | ||
| December 2 | Adic Formalism | |
| Lefschetz Fixed Point Theorem |
Resources:
- Number Theory Learning Seminar at UCLA, summer 2022.
- Étale Cohomology Learning Seminar at Oxford, spring 2021.
- Étale Cohomology Seminar at EPFL, 2018-2019.
- Daniel Litt’s course on Étale Cohomology and the Weil Conjectures at UGA, fall 2020.
- Bhargav Bhatt’s course on Étale Cohomology at Michigan, fall 2011.
- The Stacks Project, and Aise Johan de Jong’s original course on Étale Cohomology at Columbia, fall 2009.