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Sure it will - as long as you make sure you're buying that lens with a Nikon fit - most "3rd party" lenses put different fits on their lenses to make sure they correspond exactly with the requirements of each camera make - specifically the location of all the contacts between lens and camera.
The only problem I can see is that, as far as I can tell, Sigma make a 10-20mm f/4 - 5.6 and a more expensive 10-20mm f/3.5 (both lenses are for Canon, Nikon, Pentax and Sony). There seems not to be a "3.5 to 5.6".
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