In 1985, R. Rumely established a local-global principle for algebraic diophantine equations. Since then, several generalizations, variations and strengthenings have been proven by L. Moret-Baille, P. Roquette, B. Green, F. Pop and (in 2002) by A. Tamagawa. The first talk will describe these different results and explain the connections between them, whereas the second talk will outline the proof of Tamagawa's extension of the theory.