  Abridged: A photometric sample of ~7100 V<25.3 Lyman break galaxies (LBGs)
has been selected by combining Subaru/Suprime-Cam BVRci'z' data with deep
GALEX/NUV imaging of the Subaru Deep Field. Follow-up spectroscopy confirmed 24
LBGs at 1.5<z<2.7. Among the optical spectra, 12 have Ly-alpha emission with
rest-frame equivalent widths of ~5-60AA. The success rate for identifying LBGs
as NUV-dropouts at 1.5<z<2.7 is 86%. The rest-frame UV (1700AA) luminosity
function (LF) is constructed from the photometric sample with corrections for
stellar contamination and z<1.5 interlopers. The LF is 1.7+/-0.1 times higher
than those of z~2 BXs and z~3 LBGs. Three explanations were considered, and it
is argued that significantly underestimating low-z contamination or effective
comoving volume is unlikely: the former would be inconsistent with the
spectroscopic sample at 93% confidence, and the second explanation would not
resolve the discrepancy. The third scenario is that different photometric
selection of the samples yields non-identical galaxy populations, such that
some BX galaxies are LBGs and vice versa. This argument is supported by a
higher surface density of LBGs at all magnitudes while the redshift
distribution of the two populations is nearly identical. This study, when
combined with other star-formation rate (SFR) density UV measurements from LBG
surveys, indicates that there is a rise in the SFR density: a factor of 3-6
(3-10) increase from z~5 (z~6) to z~2, followed by a decrease to z~0. This
result, along with past sub-mm studies that find a peak at z~2 in their
redshift distribution, suggest that z~2 is the epoch of peak star-formation.
Additional spectroscopy is required to characterize the complete shape of the
z~2 LBG UV LF via measurements of contamination and accurate distances.
