Lightest all mountain ski is most certainly going to be a touring ski of some kind. Many uber-lightweigh touring skis can rip the whole mountain, but will never be as damp as a resort specific ski.
Agree with
@Jim McDonald the Kore is in the running for a resort ski. Less weight than that and you're pretty squarely in the the "touring" category. For a touring ski -- there are tons. And many that most resort skiers won't find the top end of. Salomon mtn explore 88 would be ~1200g / ski. Blizzards Zero G 85 similar and stiffer at ~1000g per ski. The 85 is an impressive, though very traditional ski. The Salomon mtn is far more easy going and willing to make a variety of turn shapes while still having a decent top end for more skiers.
Personally, if I had to go to one ski for aboslutely everything (touring and inbounds), I could be happy on my 1600g 182 Praxis Yetis -- though I'd probably knock of the flex stiffness a bit. Keith would probably make you a set in 162 that'd weight south of 1400g.
Don't get hung up on radius. Most every manufacturer measures differently, and while its a general guide, without knowing a skis taper length, how the sidecut is shaped, and rocker profile, it doesn't tell you the whole story of how quick it can turn. My 34m radius skis are far easier to pivot quickly in trees than my 18m radius ones.
tl;dr: Tell us more about how and where you ski if you want a useful recommendation. Otherwise you can get stupid light, even in the 85-90mm category.