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Unformatted text preview: " ,r ,ex~0 it follows that the plinear endomorphism of R"f, ((gx) induced by the pth power mapping (gx~ d~ x corresponds via the coboundary iso morphism (2.3.7.2) to the plinear endomorphism of R" + 17z, (d~p ( d)) induced by the composite (gp(d) P'thp0we, ~e(pd) HP' ,~p(__t0. This permits the calculation of the HasseWitt matrix of a hypersurface: (2.3.7.14) Algorithm. Assumptions as in (2.3.7.0) and (2.3.7.12), the Hasse Witt matrix in dimension n of a smooth hypersurface X cP~ +1 defined by an equation H=H (X1 . ... , Xn+ E)~F(S , (.gs)[X 1 . .... Xn+2] may be com puted with respect to the basis {m(W)[~.Wi=d, W/>0 for aU i} of R" f, ((gx) as follows: Raise H to p 1st power, and write it explicitly as a sum of monomials (2.3.7.15) H p 1 =}" AvX v. 3*...
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 Fall '11
 NormanKatz

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