Tate twist
In number theory and algebraic geometry, the Tate twist, named after John Tate, is an operation on Galois modules.
For example, if K is a field, GK is its absolute Galois group, and ρ : GK → AutQp is a representation of GK on a finite-dimensional vector space V over the field Qp of p-adic numbers, then the Tate twist of V, denoted V, is the representation on the tensor product V⊗Qp, where Qp is the p-adic cyclotomic character. More generally, if m is a positive integer, the mth Tate twist of V, denoted V, is the tensor product of V with the m-fold tensor product of Qp. Denoting by Qp the dual representation of Qp, the -mth Tate twist of V can be defined as
