Why wouldn't a giant AC work? Admittedly, you'd need to connect it to the Earth, not just "point it" at us. But an AC is basically a system that uses energy to move heat around; the trick is building one that puts the warm-air exhaust outside the lower atmosphere and gives it escape velocity.
For instance, as long as we're talking mad science, if we could build a space elevator with a big pool of water at the upper end as its counterbalance, cooled by evaporating into space (and maybe by contact with the upper atmosphere?), with a series of tubes connecting the pool with the sea below, then we could run an AC cycle: send warm seawater up, get almost-freezing water down. Of course we'd need a huge throughput to affect global temperature, but the principle is sound :-)
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They could send information in form of radiowaves and it could be description of unfriendly AI
What probability do you assign to this happening? How many conjunctions are involved in this scenario?