Question

does voltage amplification go against the conservation laws?

Answer 1

You mean like in a transformer? No. There is no conservation of Voltage. Conservation of Energy is taken care of because the current goes down by the same factor that the voltage goes up, in the ideal case.

Answer 2

Even in amplifiers.i.e Active device based amplifiers this doesnt go against the conservation of energy because the necessary power is supplied by the power supply to which the amplifier is plugged