Symplectic involutions of \(K3\) surfaces act trivially on \(\mathrm{CH}_0\) (Q1946053)

Let \(S\) be an algebraic \(K3\) surface. A holomorphic involution \(\iota:S\to S\) is called symplectic if it preserves the holomorphic symplectic \(2\)-form on \(S\). The main theorem of this paper is that every such involution acts as the identity on the Chow groups of zero cycles. This is a special case of a well-known conjecture of [\textit{S. Bloch}, Lectures on algebraic cycles. 2nd ed. New Mathematical Monographs 16. Cambridge: Cambridge University Press (2010; Zbl 1201.14006)].