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By Alan (-oks) Sperber and Steven I. (-mn


Dwork cohomology, de Rham cohomology, and hypergeometric functions. (English summary) Amer. J. Math. 122 (2000), no. 2, 319–348.1080-6377 Let S be a smooth, equidimensional C-scheme, X a smooth, equidimensional S-subscheme of relative dimension N and Y ⊂ X a smooth, closed S-subscheme of codimension r. Let E be a locally free OX-module of finite rank with an integrable connection ∇: E → Ω1 ⊗OX X/C E. Let j: Y ↩ → X be the inclusion and let ∇: j ∗ (E) → Ω 1 Y/C ⊗OY j ∗ (E) be the pullback of ∇ to a connection on j ∗ (E). The authors consider the problem of computing the Gauss-Manin connection on the de Rham cohomology sheaves: H n DR(Y/S, (j ∗ (E), ∇Y)). They treat the case where S, X, Y are all affine. Their main result is as follows. Let X = Spec(A) and f1, · · · , fr ∈ A. Let y1, · · · , yr be indeterminates and consider Ar X = Spec(A[y1, · · · , yr])

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Year: 2013
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