Birationally rigid Fano complete intersections

We prove that general Fano complete intersections V = Vd(1),(...),d(k) =F-1 boolean AND ... boolean AND F-k subset of p(M+k), where F-i subset of p(M+k) is a hypersurface of degree d(i) greater than or equal to 2 and the integers d(1),...,d(k) satisfy the relation d(1) + ... + d(k) = M + k (so that V is of index 1) are birationally superrigid for M greater than or equal to 2k + 1, k greater than or equal to 2. In particular, they cannot be fibered by a rational map into uniruled varieties (over a positive-dimensional base), each birational map (X): V - - --> V-1 onto a Fano variety V-1 with Q-factorial terminal singularities and rk Pic V-1 = 1 is biregular. The groups of birational and biregular self-maps coincide: Bir V = Aut V. The proof is based upon the method of maximal singularities and the techniques of hypertangent systems.