Abstract
Bloch [1] defined the formal completion of the group of 0-cycles modulo rational equivalence on a surface X and studied it in case X is defined over an algebraic number field. In this paper we investigate in detail the situation for ground fields which are extensions of Q of finite transcendence degree. We look in particular at the kernel of the formal analogue of the Abel-Jacobi mapping from Chow group to Albanese variety. It turns out that the influence of the derivations of the ground field k can be described completely in terms of the Gauss-Manin connection on H DR 2( X/ k).
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