By A. Campillo
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Additional resources for Algebroid Curves in Positive Characteristics
E--. . . D + (X) I 2) glueing 17-I(o) actually a divisor) Proj(k[~ 1 ..... ~N]) togeti~er is a c l o s e d isomorphic ' I in the obvious k-subscheme to the , ~ . +t M 2 , inclusion XN] X- I the type, ( 19 ) ) : Spec( A[ and ). of f i n i t e O. We n e e d (Bennet, (or a graded projective and the manner. fl (M) ,, BIM(A) II5 II ~ n ProJ(nO__oMJMn+l) is induced by the natural co ~ Proj( graded n e0 @ M n=o Thus, onto to such a point (al the ,... the closed directions O' ,aN). n+l n=o M points of J7-1(0) the origin represented scheme homomorphism > through may The ring ~ M n) n::o 7"1-1(O) correspond in by is .
Algebraic some by in points that every characteristic with fact k((x)) Hence, and in fundamental exponents result t' t proof. zero of unity element the the is of replace each completes of between root characteristic Waerden, of if the k((t))/k((Xl) a relation curves negative This (Van only } 2 ~ i there follows prime a One expressed number is This algebroid It , prove primitive, k. - n <~ r i ] extension a divisor contradictory. t q , where of if PN] .... We s h a l l not p of Now, not that of ) r31 .....
10. it . )=0 I + . the expansion the for i-th ~Y Z J , j+t proofs basis by j
Algebroid Curves in Positive Characteristics by A. Campillo