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co . 2 . Let G be a c ompact g roup and le t X b e the spac e of c onjugacy c las s e s of G (i. e . the quotient spac e of G by the equi ­ valenc e relation induc ed by inner automorphi sm s of G ) . I. I. I. -equidi s tribute d if and only if for any irr educ ible characte r X of G we have 1 n lim r; X (x .

W e have alr eady £ More pre cis ely, let v I Supp ( m ) , and le't fv I b e an idHe which is a uniformizing parameter at v , and which is equal to 1 everywher e els e ; let F = £ (f ) b e the image o f f in Sm (Q ) . 1 }. 1 ' whe r e II - 1 2 AB E LIAN 1 - ADIC R E PR E S E NT A T IO NS c) (d . Chap . I , P r oof. 2. 3) S1 i s e qual t o (r e s p . ab ln G F th en th e F r ob e n ius e l e ment ' F v E Sm v £ ' l (Q ) . It i s kn own that th e c l a s s f i e l d i s om o r ph i s m K map s Supp (m ) U � !!

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Abelian L-Adic Representations and Elliptic Curves (Advanced Book Classics) by Jean Pierre Serre


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