#arithmeticgeometry/rationalpoints
17:00
 What is a local fields?

What is a global field?
 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?
 What is the Jacobian of a curve?
 What is the genus of a curve?
 What is a torsor?
 What is a complete intersection?
 What are some examples of \(p{\hbox{}}\)adic fields?
 What is a SeveriBrauer variety?
 What is Hensel’s Lemma?

What is quadratic reciprocity?
 Conics over global field fail to have rational points at an even number of places?
 What is a ramified and unramified extensions?
 What is a split prime?
 Interpretation of Weil Conjectures : has lots of points over big enough extensions?
 What is the Hasse principle?

What are points in the adeles?
 Product of \(K_v\) points!
 What is the Brauer group?
 What is a central simple algebra?
 What are the main theorems of class field theory?
 Why is the following SES important? See Unsorted/rational points. \begin{align*} 0 \to \mathop{\mathrm{Br}}k \to \oplus_v \mathop{\mathrm{Br}}k_v \to {\mathbf{Q}}/{\mathbf{Z}}\to 0 .\end{align*}
 What is a Unsorted/model of a scheme?
 What is a special fiber?