Grothendieck's period conjecture holds for Kummer surfaces associated to squares of CM elliptic curves.
Tate, Algebraic cycles and poles of zeta functions, Arithmetical Algebraic Geometry, Harper & Row, 93-110 (1965)
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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.