Unformatted text preview: .., 1) in f, (f2~rTs2), ai(2)~Z[~.] [1/d(lAa)], we have (2.3.8.3) ~ai(2) ~ (G(2))=0 in Z [[21]], whereG(2)EZ[1][[21]]istheseries (2.3.8.4) a(R)=(d2)I ~ (1/d)a'"(d 1/d)a a! . ..a! (2.3.8.5) (2.3.8.6) 1~ ad . Remark. In fact, "the" differential equation satisfied by co is (Z(' d,"' as may be deduced from 123 a] and an immediate calculation shows that indeed [ d ~ d1 (2 d ~ d1 (2.3.8.7) ~d2! (G(2)) = d2! (2G(2)). (2.3.9) We refer to forthcoming works of B.Mazur for the congruence relations between the higher HasseWitt matrices and the zeta function, which generalize the "ordinary" congruence formula [251. 2.4. The Question of Quasieoherence of the Conjugate Spectral Sequence (2.4.0) We return now to the geometric situation of 1.0, and, to fix ideas, we suppose that S is affine. The conjugate spectral sequence (2,4.0.1) E~2'b=Raf,(Jfb(f2[/s(logD))) =~ Ra+bf, (~/s(1Og D))...
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 Fall '11
 NormanKatz
 Algebraic geometry, Algebraic Solutions of Differential Equations

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