Verschiebung operator

Examples

• If G is the discrete group with n elements over the finite field F_p of order p, then the Frobenius homomorphism F is the identity homomorphism and the Verschiebung V is the homomorphism . Its dual is the group scheme of nth roots of unity, whose Frobenius homomorphism is and whose Verschiebung is the identity homomorphism.
• For Witt vectors the Verschiebung takes to.
• On the Hopf algebra of symmetric functions the Verschiebung V_n is the algebra endomorphism that takes the complete symmetric function h_r to h_r/n if n divides r and to 0 otherwise.