T ate ▁theory ▁ ▁K enk ichi ▁I was awa ▁independently ▁discovered ▁essentially ▁the ▁same ▁method ▁( without ▁an ▁analog ▁of ▁the ▁local ▁theory ▁in ▁T ate ' s ▁th esis ) ▁during ▁the ▁Second ▁World ▁War ▁and ▁announced ▁it ▁in ▁his ▁ 1 9 5 0 ▁International ▁Congress ▁of ▁Mathemat icians ▁paper ▁and ▁his ▁letter ▁to ▁Jean ▁Die ud onn é ▁written ▁in ▁ 1 9 5 2 . ▁Hence ▁this ▁theory ▁is ▁often ▁called ▁ ▁I was awa – T ate ▁theory . ▁I was awa ▁in ▁his ▁letter ▁to ▁Die ud onn é ▁derived ▁on ▁several ▁pages ▁not ▁only ▁the ▁mer omorphic ▁continu ation ▁and ▁functional ▁equation ▁of ▁the ▁L - function , ▁he ▁also ▁proved ▁fin iten ess ▁of ▁the ▁class ▁number ▁and ▁Dir ich let ' s ▁theorem ▁on ▁units ▁as ▁immediate ▁by products ▁of ▁the ▁main ▁computation . ▁ ▁The ▁theory ▁in ▁positive ▁characteristic ▁was ▁developed ▁one ▁de cade ▁earlier ▁by ▁Ernst ▁W itt , ▁Wil fried ▁Sch mid , ▁and ▁O sw ald ▁Te ich m üller . ▁ ▁I was awa - T ate ▁theory ▁uses ▁several ▁structures ▁which ▁come ▁from ▁class ▁field ▁theory , ▁however ▁it ▁does ▁not ▁use ▁any ▁deep ▁result ▁of ▁class ▁field ▁theory . ▁ ▁General is ations ▁I was awa – T ate ▁theory ▁was ▁extended ▁to ▁the ▁general ▁linear ▁group ▁GL ( n ) ▁over ▁an ▁algebraic ▁number ▁field ▁and ▁autom orph ic ▁representations ▁of ▁its ▁ad el ic ▁group ▁by ▁Roger ▁G ode ment ▁and ▁Her vé ▁Jac