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}