Grothendieck's period conjecture holds for Kummer surfaces associated to squares of CM elliptic curves.
Bloch, K2 of Artinian Q-algebras, with application to algebraic cycles, Comm
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Grothendieck's period conjecture for Kummer surfaces of self-product CM type
Grothendieck's period conjecture holds for Kummer surfaces associated to squares of CM elliptic curves.