  We give sufficient conditions for cohomological flatness (in dimension 0)
over discrete valuation rings, generalising a classical result of Raynaud in
two different ways. The first is an extension of Raynaud's numerical criterion
to higher dimensions. The second is a logarithmic criterion: we show that a
proper, fs log smooth morphism to a log regular discrete valuation ring is
cohomologically flat in dimension 0. We apply this latter result to curves and
torsors under abelian varieties with good reduction, providing necessary and
sufficient conditions for the log smoothness of their regular models over
arbitrary discrete valuation rings.
