  We consider local-global principles for rational points on varieties, in
particular torsors, over one-variable function fields over complete discretely
valued fields. There are several notions of such principles, arising either
from the valuation theory of the function field, or from the geometry of a
regular model of the function field. Our results compare the corresponding
obstructions, proving in particular that a local-global principle with respect
to valuations implies a local-global principle with respect to a sufficiently
fine regular model.
