Voltage
But you can't "supply 0.1V to the base" - voltages do not exist at isolated points, but only with respect to a reference. In this case, it is the voltage across the base- emitter junction (Vbe - the "v" should normally be written lower-case in this context, but I'm afraid that would look confusing here) which controls, through the transistor's "transconductance" (Gm, again normally a lower-case G with a subscript m), the collector current. I am afraid you are confusing the DC bias conditions (and the resulting DC forward drop across the B-E junction, VBE) with the small-signal voltages. With the transistor biased in the active mode, and that 0.6-0.7V drop you mentioned established, yes, a relatively small *AC* signal across this junction DOES control the collector current.
Bob M.