I am not a lawyer, nor have I ever been a soldier. So I have never studied the Geneva Conventions. However, I just tried to quickly look at them on the Web. There are four Conventions, last amended in 1949. Then there are two additional Protocols added in 1977. Then ... they had to cut down a FOREST to make the paper to print all the additional conventions and protocols and specific prohibitions and exceptions. Like, you can't use a laser specifically to blind someone (if he gets blinded while he's being burned in half, tough luck). You can't use bullets that expand or flatten on entry, they cause unnecessary injury and suffering. Likewise any explosive or incendiary munition weighing less than about a pound (400 grams, to be precise).
But I did not see anything specifically prohibiting (or even mentioning) any particular calibre of bullet. Nor did I find anything prohibiting use of any projectile (except the aforementioned dum-dums) against people (soldiers).
I did find an
article by a former Air Force member
, who says he studied the Conventions, instructed others concerning them, and acted in accord with them as part of his duties as a fire control officer in Iraq. He states that the idea that the Conventions prohibit use of .50-calibre weapons against people, is a long-standing and widely-spread rumor, and that the Conventions contain no such prohibition. His article also dispels several other misconceptions about military terms such as "free-fire area" and explains what they actually mean.
So. That's two sources: my own (admittedly cursory) research, and someone who does know the Conventions in detail. Standard disclaimer about double-checking anything you find on the Web, applies here of course. That's why I looked up the Conventions myself.
BTW, I also ran into an anecdote about Marine Corps training, where the soldiers are told that the Geneva Conventions prohibit using a .50 on people, .50's are for equipment, and for those who are wondering, helmets and uniforms are equipment. This story also appears aprocryphal.