Isometries of ideal lattices and hyperk\"ahler manifolds
  We prove that there exists a holomorphic symplectic manifold deformation equivalent to the Hilbert scheme of two points on a K3 surface that admits a non-symplectic automorphism of order 23, that is the maximal possible prime order in this deformation family. The proof uses the theory of ideal lattices in cyclomotic fields. 
Samuel Boissi\`ere, Chiara Camere, Giovanni Mongardi and Alessandra   Sarti
math.AG