2021-03-17

#subjects/arithmetic-geometry/rational-points

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?
  • 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 {\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