---
date: 2021-03-17
tags: [ web/quick-notes ]
---


# 2021-03-17

#arithmetic-geometry/rational-points

## 17:00

- What is a [local fields](local%20fields)?
- What is a [global field](global%20field.md)?
  - Why are these generally more difficult than local fields?
- What is a field that is not local or global?
- What is a fibration of varieties?
- What is a [del Pezzo surface](del%20Pezzo%20surface)?
- What is the [Jacobian](Jacobian.md) of a curve?
- What is the genus of a curve?
- What is a [torsor](torsor.md)?
- What is a [complete intersection](complete%20intersection)?
- What are some examples of $p\dash$adic fields?
- What is a [Severi-Brauer variety](Severi-Brauer%20variety)?
- What is [Hensel's Lemma](Hensel's%20Lemma.md)?
- What is [quadratic reciprocity](quadratic%20reciprocity.md)?
  - Conics over [global field](global%20field.md) fail to have rational points at an even number of places?
- What is a [ramified](Unsorted/ramification%20index.md)  and unramified extensions?
- What is a split prime?
- Interpretation of [Weil Conjectures](Weil%20Conjectures.md) : has lots of points over big enough extensions?
- What is the [Hasse principle](Unsorted/Hasse%20principle.md)?
- What are points in the [adeles](adeles.md)?
  - Product of $K_v$ points!
- What is the [Brauer group](Brauer%20group.md)?
- What is a [central simple algebra](central%20simple%20algebra.md)?
- What are the main theorems of [class field theory](class%20field%20theory.md)?
- Why is the following SES important? See [Unsorted/rational points](Unsorted/rational%20points.md).
\[
0 \to \Br k \to \oplus_v \Br k_v \to \QQ/\ZZ \to 0
.\]
- What is a [Unsorted/model of a scheme](Unsorted/model%20of%20a%20scheme.md)?
- What is a [special fiber](special%20fiber.md)?