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

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

2010-09-22

arxiv.org/abs/1009.4371v1

Mathematics

Algebraic Geometry

8 pages

Scientific paper

For a projective K3 surface X we introduce the dense triangulated subcategory
S^* of the bounded derived category D^b(Coh(X)) of coherent sheaves on X that
is generated by spherical objects. For a K3 surface X over \bar Q it is shown
that S^* admits a bounded t-structure if and only if the Bloch-Beilinson
conjecture holds for X, i.e. CH^2(X)=Z.

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