Let X be a complex projective K3 surface, and let T(X) be its transcendental lattice; the characteristic polynomials of the isometries of T(X)  induced by automorphisms of X are powers of  cyclotomic polynomials. Which powers of cyclotomic polynomials occur ? The aim of this talk is to answer this question, as well as related ones, and give an alternative approach to some results of Kondo, Machida, Oguiso, Vorontsov, Xiao and Zhang.

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