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Algebraic Solutions of Differential Equations
39
(2.4.1)
In the special case when S is a schema of characteristic p, the
conjugate spectral sequence (2.4.0.1)
is
the second spectral sequence of
hypercohomology for the (,0xcp)linear complex
F,(O}/s(log D))
on X ~p),
and the functors R"J~ ~. Because f~P):
X ~p), S
is quasicompact and
separated, the various
F,(f~x/s(log D))
are quasicoherent (gxmodules,
and
F,(d)
is Cxc~,linear, the second spectral sequence (2.4.0.8) of the
Cech bicomplex
does
map isomorphically to the conjugate spectral
sequence (2.4.0.9), which
is
a spectral sequence of quasicoherent (_9
s
modules.
The simple interpretation of the conjugate spectral sequence in
characteristic p as the second spectral sequence of the Cech bicomplex
(2.4.0,3) makes possible effective calculations, as we shall see. On the
contrary, the conjugate spectral sequence over C remains in shadow.
3. The Main Technical Result on the pCurvature
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
 Fall '11
 NormanKatz

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