Lectures on the Hasse-Minkowski theorem.

  • Lecture 1, where we discuss quadratic form, their equivalence and why any form is equivalent to a diagonal one.
  • Lecture 2, where we discuss p-adic integers.
  • Lecture 3, where we discuss general p-adic numbers and complete squares.
  • Lecture 4, where we discuss quadratic forms with p-adic coefficients and state the Hasse-Minkowski theorem.
  • Problem set, featuring one problem on Lecture 1, one problem on Lecture 3, and one problem on Lecture 4. The latter proves the theorem from Section 0 of Lecture 4 for p=2 and uses the first two problems.
  • Lecture 5, where we partly prove the main theorem.