Commutative Formal Groups by Prof. Dr. Michel Lazard (auth.)

By Prof. Dr. Michel Lazard (auth.)

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14 e. I varieties because, for a n y b a s i c homomoprhism starting For from e : Z ~ K, Z, m a y be instance, the e l e m e n t a r y and m o r p h i s m s said S y m n ( X l,x 2 ..... 19 T. e. c. m. o. r. p. h. i. s m morphism, to be deserve there a special is a u n i q u e the c h a n g e s o f rings, automatic. Symn: = Dn ~ Dn is d e f i n e d (Xix i , Z i < j x i x j ..... x l - , . t theorem. e. a morphism f(x I ..... 18 symmetric ring so that the m o r p h i s m symmetric over f : Dn ~ V verifying (I) .....

T theorem. e. a morphism f(x I ..... 18 symmetric ring so that the m o r p h i s m symmetric over f : Dn ~ V verifying (I) ..... 20 of the g reduces a formal module out I ..... n such . 17) , the b a s i c V, this symmetric ring K may theorem polynomials. remain unde- fined. CHAPTER FORMAL GROUPS I. 2 admits ables on G corresponding tities G ways in the c a t e g o r y , alternative by giving, theory qroups, products. with some of group (resp. (resp. commutative G n ~ G, word-functions or c o m m u Anyhow, extra a struc- descriptions.

Now, ~(1) ~)K1 • rinqs series , fj(x) unchanged, presently we denote the same f : D K(I) ~ D(J) K have We there ~ DKt of m o d e l s over K de fin in q precisely, f. M o r e = E~ c 3 , ~ x (~o~). V) (A') e*A' ~ nil(K) variety for a n y )X to e v e r v , j ~ J, functor the by 9. o~. the c a t e g o r y over K'. Note that , ~,d~ . functor variety over A'~ the K - a l g e b r a A' , m u l t i p l i c a t i o n corresponds e. to the c a t e g o r y K. 2 vectors . (1) of the. f o r m a l (fj)j~j will K' w i t h To e v e r y m o r p h i s m by applyinq taDgent ~'V .

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