ABSTRACT
A diophantine equation cannot be solvable over the field of rationals if it has no p-adic solutions (since Q ⊂ Qp). In this chapter we will prove that quite often the converse implication holds to be true as well. This means that the information on solvability of certain equations over all Qp, p ≤ ∞, gives information on the solvability over Q. We will prove a special case of this principle, the celebrated theorem of Hasse-Minkowski, for ternary quadratic forms.
