3
Three things you think you understood.
Now running · Meeting 3
Étale Cohomology Seminar 2026
The five-meeting pilot is underway.
We follow Daniel Litt's Étale Cohomology and the Weil Conjectures. Videos, notes, references, and AI tools support individual preparation. We meet weekly to do what requires other mathematicians: question, verify, challenge, explain, review, and decide together what is worth remembering.
Fridays · 17:00-18:30 Lima · 19:00-20:30 Brasília
Online via Google Meet
This Friday: Meeting 3 · September 18, 2026 · Sites, sheaves, and the étale and fppf topologies
An imaginative illustration of the conversations and ideas surrounding the development of étale cohomology.
What this is
A serious seminar, not another notes archive.
The seminar is a public, collaborative pilot for undergraduate, master's, PhD, and other mathematically mature participants who want to study the first part of Litt's course together.
The repository records what the community contributes beyond the lectures: examples, non-examples, verification, peer review, proof digestion, useful friction, attribution, and a small shared toolkit.
Read the full project README →Why another seminar?
Explanations are abundant. Human mathematical judgment is scarce.
Videos + books + AI
explanation · information · examples · assistance
The seminar
verification · discussion · judgment · responsability · shared understanding · mathematical community
We are not meeting because mathematical explanations are scarce. We are meeting because human mathematical attention, criticism, trust, and shared understanding are scarce and valuable. Our philosophy is inspired in part by questions raised in Terence Tao's Mathematics in the Age of AI.
Read our full seminar values →How it works
3 + 2 + 1 + E + R + P
2
Two points of mathematical friction.
1
One question worth discussing with humans.
E
One example or non-example that clarifies a definition or theorem.
R
Review one mathematical contribution made by another participant.
P
Problem of the Week. Engage seriously with one common problem. A partial solution, failed approach, or useful observation may be as valuable as a complete solution.
candidate
peer checked
discussed
shared toolkit
Candidate examples and proofs are proposed, checked by another person, discussed by the seminar, and only then may enter our shared toolkit.
Read the contribution guide →Problem of the Week
Problems are for thinking, not merely for obtaining answers.
AI can often produce a candidate solution. Our goal is to understand why a solution works, where the key idea lies, what fails in unsuccessful approaches, and whether another mathematician can verify and explain it.
try
get stuck
use references/tools
reconstruct
peer review
discuss
digest
Examples matter
The best example is the one that makes the mathematics clearer.
Every participant is encouraged to commit the example or non-example they found most illuminating. It does not need to be the most sophisticated example in the room.
GitHub helps us preserve who contributed it, how it was checked, what sources were used, whether AI or software helped, and how the contribution changed after review.
See the repository →Who can participate?
One mixed-level seminar.
You do not need to understand 100% of every lecture before coming to the meeting.
Undergraduate
Definitions, examples, intuition, and good questions.
Master's
Also proof architecture, hypotheses, and independent examples.
PhD and beyond
Also context, criticism, reviewing, connections, and mentoring without dominating.
Serious curiosity and preparation matter more than academic seniority.
Read the detailed expectations →Five-meeting pilot
The first block follows Litt's first five lectures.
- Meeting 1 Aug 28 · Weil conjectures and motivation. Materials in progress.
- Meeting 2 Sep 4 · Étale morphisms and introduction to sites. Read Meeting 2 notes.
- Problem session Sep 11 · Exercises from Litt's Lecture 2: standard étale morphisms, the power map on Gm, 2-out-of-3, and completed local rings. Review the exercises.
- Meeting 3 Sep 18 · Sites, sheaves on sites, examples of sites, and the étale and fppf topologies. Read Meeting 3 notes.
- Meeting 4 Sep 25 · Morphisms of sites and fppf descent I.
- Meeting 5 Oct 2 · fppf descent II and the beginning of the study of the category of sheaves.
Fridays, 17:00-18:30 Lima / 19:00-20:30 Brasília. Online via Google Meet.
After the fifth meeting, the group decides whether and how to continue.
Each week
Prepare individually. Verify together.
Before
watch → read → try the problem → use tools → contribute → review
During the 90-minute meeting
- 0-15
- collective reconstruction
- 15-30
- friction board
- 30-50
- common Problem of the Week
- 50-70
- example / theorem / proof deep dive
- 70-80
- what should survive?
- 80-90
- connections, community, next week
The opening reconstruction is AI-free and notes-closed.
AI and tools
AI is welcome. Responsability remains human.
We use AI and mathematical software freely for preparation, while keeping human responsability, verification, reviewing, attribution, and collective digestion at the center of the seminar.
- Disclose substantial tool use.
- Make contributions easy for other humans to review.
- Human responsability remains with mathematical claims.
- Properly attribute mathematical sources and other people's ideas.
"GPT told me so" is not mathematical verification.
Read the values →