Lectures on algebraic cycles

By J. Lewis. 2001

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Curves and cycles on K3 surfaces (2013, background): “Here, c X ∈ CH 2 ( X ) is the distinguished class of degree one introduced by Beauville and Voisin in [BV04].”
Motives and representability of algebraic cycles on threefolds over a field (2008, background): “Since zero-cycles on the surface Xη̄ are representable, it follows that its diagonal is balanced by curves, [5], so the motive M(Xη̄) is finite-dimensional, [10], and the group H(2)(Xη̄)(1) is algebraic, [1].”
Lectures on K3 Surfaces (2016, background): “See Roitman’s original article [509] and Bloch’s version [65, 66] showing that there is no torsion prime to the characteristic.”
The Fourier Transform for Certain HyperKähler Fourfolds (2013, background): “It should be mentioned that, as explained in [8], (1) is expected to be the splitting of a Bloch–Beilinson type filtration on CH∗(A).”
Chow Rings, Decomposition of the Diagonal, and the Topology of Families (2014, background): “20 is a vast generalization of the Bloch conjecture for surfaces [13].”
The Generalized Hodge and Bloch Conjectures are Equivalent for General Complete Intersections, II (2011, background): “10]), which was formulated by Bloch [1] in the case of surfaces, and can be stated as follows:”
BLOCH'S CONJECTURE FOR CATANESE AND BARLOW SURFACES (2012, background): “[7]) Let Γ ∈ CH(2)(Y ×X), where Y is smooth projective and X is a smooth projective surface.”