2021-03-17

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 Severi-Brauer variety?
• What is Hensel’s Lemma?
• 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 {\mathbb{Q}}/{\mathbb{Z}}\to 0 .\end{align*}
• What is a Unsorted/model of a scheme?
• What is a special fiber?
#web/quick-notes #subjects/arithmetic-geometry/rational-points