There are some credible war crimes accusations (in fact, some pretty flagrant war crimes), but the most critical crime is actually not a war crime, but one precedent to their being a war at all, the crime of aggression.
Starting a war is generally what is known in modern international law as the crime of aggression (in the language of the Nuremberg Charter, this was, “crimes against peace”, the first listed category of crimes subject to the tribunal, above war crimes and crimes against humanity.)
Rudolph Hess, notably, was convicted and imprisoned for life solely for this crime.
