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Unformatted text preview: and by (126.96.36.199) the formation of its E 2 term commutes with arbitrary change of S'~ S. The result follows by (188.8.131.52). (2.3.3) We are now in a position to explain the terminology "conjugate" spectral sequence. With the assumptions of proposition (2.3.2), suppose further that S is the spectrum of a field K of characteristic p, and that the divisor D is void. The Hodge ~ De Rham spectral sequence (184.108.40.206) E~' b = H b (X, ~X/K) =*" Ha + b (X, ~"~'/K) being degenerate at Et, we have (220.127.116.11) g~ (H n (X, f2~/r ) ) ~ H"- ~ (X, f~a'/~)- The degeneracy at E2 of the conjugate spectral sequence (18.104.22.168) co,E~2'b =F~H~(X, f2~,/~) =~ H~+~(X, f2~/r) which we prefer to rewrite as (22.214.171.124) r =H~(X ~p~, O~c~/K) =~ Ha+b(X, f2~//~), gives an isomorphism (126.96.36.199) g~on n~ (X, f2~c/K ) ~-- H a (X ~p~, f~}?~,~/K) Putting together (188.8.131.52) and (184.108.40.206) (for X tp~) we find an isomorphism (220.127.116.11) g~o H"(X, f2~/r)"~g~-~ H~(X ~v~, I2],~,/r ) ....
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