0. PRELIMINARIES.
All material presented in this section (notation, conventions,
definitions, fixed normal forms etc.) is obligatory for all the subse-
quent text. It will remain unchanged and valid throughout.
0.1. NOTATION AND CONVENTIONS.
For sets of numbers we use the following notation:
I N = { 1 , 2 , 3 , . . . , INL = I N u {0} , I N = I N u {co} , Q+ = {r e Q I r 0} ,
0 oo
C L = Q U { 0 } , CL = Q u {0,co} .
0 0, oo
Throughout, R denotes a complete discrete valuation ring with ex-
ponential valuation v , satisfying the following properties:
(a) v(3) = 4 ,
(b) R does not contain a primitive third root of unity.
With R we associate the following data:
K = field of fractions of R
k = residue class field of R
n = chosen parameter of R
R = R/n^R (n I N )
n oo
- 3
d = —j , u n i t of R by h y p o t h e s i s (a)
7T
d = residue class of d in k
2
8 = X - d , irreducible in k[X] by hypothesis (b)
f = k[X]/(s)
I = {A k[X] | A i s monic and i r r e d u c i b l e } u {oo}
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