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In number theory and algebraic geometry , the Tate twist , named after John Tate , is an operation on Galois module s. For example , if K is a field , GK is its absolute Galois group , and ρ : GK → AutQp ( V ) 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 ( 1 ) , is the representation on the tensor product V ⊗ Qp ( 1 ) , where Qp ( 1 ) is the p-adic cyclotomic character ( i.e. the Tate module of the group of roots of unity in the separable closure Ks of K ) .
 person: Tate; person: John Tate; person: Tate; person: Tate
Given options, please tell me the categories of all the listed entity words.Output format is "type1: word1; type2: word2". 
Option: location, person, organization 
Text: {0} 
 Entities: Tate, John Tate, Tate, Tate 
Answer:
 person: Tate; person: John Tate; person: Tate; person: Tate