The Work of Pierre Deligne - International Mathematical Union

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48 N. M. Katz of the form Pi(T)= nV-aijT), such that the map oL*^q n loL carries the a u bijectively to the a 2n -i,j- (3) The polynomials P t (T) lie in Z[T] 9 and their reciprocal roots
The Work of Pierre Deligne 49 medean considerations into the /-adic theory without first knowing the rationality of the cofficients of the P itl Let me now try to indicate the brilliant synthesis of ideas involved in Deligne's solution of these problems. Initially, he tries to prove à priori that the P ul have rational coefficients independent of /. The idea is to proceed by induction on the dimension of Y. If Y is 77-dimensional, then Poincaré duality and the fact that the zeta function is itself rational and independent of / reduce us to treating the polynomials P Ui for i
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The Work of Pierre Deligne - International Mathematical Union

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