Global InformationVerschiebung operator information
In mathematics, the Verschiebung or Verschiebung operator V is a homomorphism between affine commutative group schemes over a field of nonzero characteristic p. For finite group schemes it is the Cartier dual of the Frobenius homomorphism. It was introduced by Witt (1937) as the shift operator on Witt vectors taking (a0, a1, a2, ...) to (0, a0, a1, ...). ("Verschiebung" is German for "shift", but the term "Verschiebung" is often used for this operator even in other languages.)
The Verschiebung operator V and the Frobenius operator F are related by FV = VF = [p], where [p] is the pth power homomorphism of an abelian group scheme.