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We give a complete account of the Schr\"odinger representation approach tothe calculation of the Weyl anomaly of ${\cal N}=4$ SYM from the AdS/CFTcorrespondence. On the AdS side, the $1/N^2$ correction to the leading orderresult receives contributions from all the fields of Type IIB Supergravity, thecontribution of each field being given by a universal formula. The correctmatching with the CFT result is thus a highly non-trivial test of thecorrespondence.Comment: 30 page

The Boundary Weyl Anomaly in the = 4 SYM/Type IIB Supergravity Correspondence