Quadratic Lattices and Genus Classes

This lecture covers the integral Hasse principle for locally representable integers by quadratic lattices, the concept of locally isometric lattices, and the Hasse-Minkowski theorem. It also discusses the Hermite-Minkowski theorem, equidistribution in the genus, and the local-global principle for lattices. The lecture concludes with the ring of adèles of Q, the ring of finite adèles, and the possible completions of Q indexed by the King of Adeles.