ate ▁tw ist ▁of ▁V , ▁denoted ▁V ( 1 ), ▁is ▁the ▁representation ▁on ▁the ▁tensor ▁product ▁V ⊗ Q p ( 1 ), ▁where ▁Q p ( 1 ) ▁is ▁the ▁p - adic ▁cycl ot omic ▁character ▁( i . e . ▁the ▁T ate ▁module ▁of ▁the ▁group ▁of ▁roots ▁of ▁unity ▁in ▁the ▁separ able ▁closure ▁K s ▁of ▁K ). ▁More ▁generally , ▁if ▁m ▁is ▁a ▁positive ▁integer , ▁the ▁m th ▁T ate ▁tw ist ▁of ▁V , ▁denoted ▁V ( m ), ▁is ▁the ▁tensor ▁product ▁of ▁V ▁with ▁the ▁m - fold ▁tensor ▁product ▁of ▁Q p ( 1 ). ▁Den oting ▁by ▁Q p ( − 1 ) ▁the ▁dual ▁representation ▁of ▁Q p ( 1 ), ▁the ▁- m th ▁T ate ▁tw ist ▁of ▁V ▁can ▁be ▁defined ▁as ▁ ▁References ▁ ▁Category : Number ▁theory ▁Category : Al gebra ic ▁geometry <0x0A> </s> ▁Jason ▁P ohl ▁( born ▁July ▁ 1 , ▁ 1 9 8 1 ) ▁is ▁a ▁cho pper ▁designer ▁who ▁works ▁at ▁Orange ▁County ▁Ch opp ers . ▁He ▁is ▁most ▁commonly ▁known ▁for ▁his ▁work place ▁being ▁the ▁subject ▁of ▁the ▁American ▁TV ▁series ▁American ▁Cho pper . ▁ ▁History ▁ ▁P ohl ' s ▁initial ▁plan ▁was ▁to ▁join ▁the ▁U . S . ▁Marine ▁Corps ▁after ▁finishing ▁high ▁school , ▁however , ▁he ▁was ▁awarded ▁the ▁August ▁Holland ▁Sch olar ship ▁and ▁decided ▁to ▁attend ▁the ▁Illinois ▁Institute ▁of ▁Art , ▁where