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N.M. Katz:
zero. This implies that for every maximal ideal m of B such that
B/m B
has characteristic p~2;, the inverse image on
B/m B
of the mapping
p(D)
vanishes, i.e., all the matrix coefficients of p (D) lie in m. Because B is a
finitely generated integral domain whose fraction field is of characteristic
zero, it follows immediately from Noether's normalization theorem that
for any infinite set 2" of prime numbers, the intersection of all maximal
ideals of B with residue characteristic in 2" is reduced to zero. Thus the
KodairaSpencer mapping (5.1.2.1) vanishes. This concludes the proof.
5.2. A Global Situation with a Group of Operators
(5.2.0)
Hypotheses as in (5.0.0), let G be a finite group, which acts as a
group of Sautomorphisms of X which are stable on D. Let g be the least
common multiple of the orders of the elements of G, and let Ao=
Z [l/g, ~g], where ~g is a primitive gth root of unity. We suppose A ~ A o.
(5.2.1)
As is wellknown (cf. [38]),
every
irreducible representation of G
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 Fall '11
 NormanKatz
 Prime Numbers, class (cf., extendi ng scalars, Frobenius automorp hism, locally free Aomodule

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