  We formulate axioms of conformal theory (CT) in dimensions $>2$ modifying
Segal's axioms for two-dimensional CFT. (In the definition of
higher-dimensional CFT one includes also a condition of existence of
energy-momentum tensor.) We use these axioms to derive the AdS/CT
correspondence for local theories on AdS . We introduce a notion of weakly
local quantum field theory and construct a bijective correspondence between
conformal theories on the sphere $S^d$ and weakly local quantum field theories
on $H^{d+1}$ that are invariant with respect to isometries. (Here $H^{d+1}$
denotes hyperbolic space= Euclidean AdS space.) We give an expression of AdS
correlation functions in terms of CT correlation functions. The conformal
theory has conserved energy-momentum tensor iff the AdS theory has graviton in
its spectrum.
