Our object is to extend earlier work [D1] on singular hypersurfaces defined over an algebraic number field to singular hypersurfaces defined over function fields in characteristic zero. A key role will be played by the results of Bertolin [B1] which in turn is based upon the Transfer Theorem of André–Baldassarri–Chiarellotto [DGS, Theorem VI 3.2]. Let h(A, x) be the generic form of degree d in n+1 variables x1, . . . , xn+1.

The area starts with Galois and Gauss Group theory and expo nential sums were the two application areas then That tradition continues Without Chevalley groups over nite elds there would have been no… Expand

Our object of study is the arithmetic of the differential modules (l) (l ∈ ℕ – {0}), associated by Dwork's theory to a homogeneous polynomial f (λ,X) with coefficients in a number field. Our main… Expand

Introduction Multiplication by Xu (Gauss contiguity) Algebraic theory Variation of Wa with g Analytic theory Deformation theory Structure of Hg Linear differential equations over a ring Singularities… Expand