Nori’s construction and the second Abel-Jacobi map

Abstract

Here a sheaf F on X is weakly constructible if X is the disjoint union of finite collection of locally closed subschemes Yi defined over k such that the restrictions F |Yi are locally constant. Beilinson ([1], Lemma 3.3) proves this fact in all characteristics of the base field. Based on Theorem 1.1 Nori shows that affine k-varieties have a kind of “cellular decomposition”. In section 2 of this note we give an exposition of the outcome if we apply this construction to etale cohomology. It can also be viewed as a partial exposition of l-adic realization of Nori’s category of motives. The main result (Theorem 2.2)