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affine algebraic closure assume automorphism Banach space biregular chain map Chapter coefficients cohomology theory cohomology transformation complex cobordism complex oriented converges Corollary curve over F Cy(t decomposition definition degree-preserving denote dilp discretely normed Dwork element equation Euler class finite dimensional fixed point theorem follows formal group formal power series fundamental points GF(q Hence homogeneous of degree homology homomorphism HQ(F hypersurface I-typical idempotent induces infinitely near point integers isomorphism k-rational k-rational divisor Lefschetz fixed point Lemma Let F line bundle linear system logarithm matrix module monomial multiplicative cohomology non-singular non-singular projective notation one-place point operators ordinary point orthonormal basis p-adic projective hypersurface proper transform prove Quillen Remark subcomplex subspace Suppose Theorem 9.l total transform typical curve typical formal group variables variety defined vector zeta function