The Chow motive of the Godeaux surface

By M. Beltrametti, F. Catanese, C. Ciliberto, A. Lanteri, C. Pedrini. 2002

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The motive of a classifying space (2014, background): “For example, the Chow motive with Q coefficients of an Enriques surface or a Godeaux surface over C is a direct sum of Tate motives [23], and so these varieties satisfy the Chow Künneth property with Q coefficients.”
Motives and representability of algebraic cycles on threefolds over a field (2008, background): “As pg(E) = 0 and S is an elliptic surface, the motive M(E) is finitedimensional, [9].”
On the derived category of the classical Godeaux surface (2012, background): “The point e0,0 has been calculated in [12].”
PROJECTORS ON THE INTERMEDIATE ALGEBRAIC JACOBIANS (2009, background): “late ﬁnite dimensionality in the sense of Kimura [14] of the Chow motive h(X) := (X,idX,0) to the representability of its total Chow group. Such problems have been tackled by Guletskii and Pedrini in [8]. They proved that for a surface S, CH0(S) is representable if and only if H2(S,OS) = 0 and the C”