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We present the results of a 2′ × 3′ (3.7 Mpc× 5.5 Mpc at z = 3, in a comoving scale) deep survey at 1.1 mm taken with ALMA in the SSA22 field (ALMA deep field in SSA22 or ADF22). Using a mosaic of 103 ALMA pointings, we observed the core region of a z = 3.09 proto-cluster, achieving an typical rms sensitivity of 60 µJy beam−1 at a resolution of 0.7 arcsec. We obtained 18 robustly detected ALMA sources (here after submillimeter galaxies, SMGs) with a signal-to-noise ratio (SNR) > 5. At least 10 ALMA SMGs have spectroscopic redshifts of z = 3.09. We find that multiple z = 3.09 ALMA SMGs contribute to two AzTEC sources, supporting that interaction may be responsible for a significant fraction of multiplicity in single-dish sources. Not only are these SMGs members of the proto-cluster but they in fact reside within the node at the junction of the 50 Mpc-scale filamentary three-dimensional structure traced by Lyman-alpha emitters (LAEs) in this field. We also find that six of the 10 ALMA SMGs host a X-ray luminous active galactic nuclei (AGN). Our results suggest that the vigorous star formation activity and the growth of super massive black holes (SMBHs) occurred simultaneously in the densest regions at z ∼ 3, which is likely to correspond to the most active historical phase of the massive galaxy population found in the core of the clusters in the present universe.