#arithmetic-geometry/rational-points
17:00
- What is a local fields?
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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 Severi-Brauer variety?
- What is Hensel’s Lemma?
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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?
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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?