[en] For an arithmetic model X of a Fermat surface or a hyperkahler variety with Betti number b₂(V otimes k-bar)>3 over a purely imaginary number field k, we prove the finiteness of the l-components of Br'(X) for all primes l>>0. This yields a variant of a conjecture of M. Artin. If V is a smooth projective irregular surface over a number field k and V(k)≠ nothing, then the l-primary component of Br(V)/Br(k) is an infinite group for every prime l. Let A¹→M¹ be the universal family of elliptic curves with a Jacobian structure of level N>=3 over a number field k supset of Q(e^2πi/N). Assume that M¹(k) ≠ nothing. If V is a smooth projective compactification of the surface A¹, then the l-primary component of Br(V)/Br(M-bar¹) is a finite group for each sufficiently large prime l