A note on the Bloch-Beilinson conjecture for K3 surfaces and spherical objects

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For a projective K3 surface X we introduce the dense triangulated subcategory S* of the bounded derived category Dᵇ(Coh(X)) of coherent sheaves on X that is generated by spherical objects. For a K3 surface X over Q it is shown that S* admits a bounded t-structure if and only if the Bloch-Beilinson conjecture holds for X, i.e. CH²(X)=Z.