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Community access to deep (i ~ 25), highly-multiplexed optical andnear-infrared multi-object spectroscopy (MOS) on 8-40m telescopes would greatlyimprove measurements of cosmological parameters from LSST. The largest gainwould come from improvements to LSST photometric redshifts, which are employeddirectly or indirectly for every major LSST cosmological probe; deepspectroscopic datasets will enable reduced uncertainties in the redshifts ofindividual objects via optimized training. Such spectroscopy will alsodetermine the relationship of galaxy SEDs to their environments, keyobservables for studies of galaxy evolution. The resulting data will alsoconstrain the impact of blending on photo-z's. Focused spectroscopic campaignscan also improve weak lensing cosmology by constraining the intrinsicalignments between the orientations of galaxies. Galaxy cluster studies can beenhanced by measuring motions of galaxies in and around clusters and by testingphoto-z performance in regions of high density. Photometric redshift andintrinsic alignment studies are best-suited to instruments on large-aperturetelescopes with wider fields of view (e.g., Subaru/PFS, MSE, or GMT/MANIFEST)but cluster investigations can be pursued with smaller-field instruments (e.g.,Gemini/GMOS, Keck/DEIMOS, or TMT/WFOS), so deep MOS work can be distributedamongst a variety of telescopes. However, community access to large amounts ofnights for surveys will still be needed to accomplish this work. In twocompanion white papers we present gains from shallower, wide-area MOS and fromsingle-target imaging and spectroscopy.

Community access to deep (i ~ 25), highly-multiplexed optical andnear-infrared multi-object spectroscopy (MOS) on 8-40m telescopes would greatlyimprove measurements of cosmological parameters from LSST. The largest gainwould come from improvements to LSST photometric redshifts, which are employeddirectly or indirectly for every major LSST cosmological probe; deepspectroscopic datasets will enable reduced uncertainties in the redshifts ofindividual objects via optimized training. Such spectroscopy will alsodetermine the relationship of galaxy SEDs to their environments, keyobservables for studies of galaxy evolution. The resulting data will alsoconstrain the impact of blending on photo-z's. Focused spectroscopic campaignscan also improve weak lensing cosmology by constraining the intrinsicalignments between the orientations of galaxies. Galaxy cluster studies can beenhanced by measuring motions of galaxies in and around clusters and by testingphoto-z performance in regions of high density. Photometric redshift andintrinsic alignment studies are best-suited to instruments on large-aperturetelescopes with wider fields of view (e.g., Subaru/PFS, MSE, or GMT/MANIFEST)but cluster investigations can be pursued with smaller-field instruments (e.g.,Gemini/GMOS, Keck/DEIMOS, or TMT/WFOS), so deep MOS work can be distributedamongst a variety of telescopes. However, community access to large amounts ofnights for surveys will still be needed to accomplish this work. In twocompanion white papers we present gains from shallower, wide-area MOS and fromsingle-target imaging and spectroscopy.