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Unformatted text preview: (x - 1)(x - 2)], with basis (188.8.131.52) 1, 1/7, l/y 2, . .., 1/y "-1 . To any n-th root of unity ~/~,, we assosciate the C(2)-automorphism of X(n; a, b, c) given by XF--~ X (184.108.40.206) y~--~ ~y. This defines an action of/~, on X(n; a, b, c). Let X denote the "identical" character of /~,, i.e., Z(~)=~, and for any integer L let X(f) denote the character of/4, given by (220.127.116.11) ;((~) (~)= ~e. This basis (18.104.22.168) of A(n; a, b, c) over B is just its "isotypique" decomposition according to the characters of/J,: (22.214.171.124) P(X(-E)) A(n; a, b, c)=y-eB = lim y-e-,, C(2)[x]. F~ 9O The de Rham cohomology group H~R(X(n; a, b, c)/C(2)) is the co- kernel of the exterior differention map (126.96.36.199) A(n; a, b, c) d , 12~(,;~,b,c)/c~ ~ because X(n; a, b, c) is affine and smooth of relative dimension one over C(2). The module f2]~,;,,h.~)/C~Z) is free over A(n; a, b, c) with basis dx. 7 Inventiones math., VoL 18...
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
- Fall '11