Intel's website has been updated and now we know the full specifications of this chip. The Core i3-8121U is listed on Intel's ARK database as a 10nm part with a Q2 2018 launch date. It' a dual-core, quad-threaded chip with a 2.2GHz base clock, 3.2GHz Turbo, 4MB cache, and a 15W TDP.
It supports dual-channel DDR4-2400 as well as LPDDR4/X-2400. One major caveat is that the Core i3-8121U has no integrated graphics, so laptops with this chip require a discrete video card. The lack of graphics is interesting, it seems like another sign of the 10nm issues.