Unformatted text preview: Then its group of automorphisms is finite. Proof Any automorphism +p determines an element Up in the group (4.2.0.15) Aut(Hz/torsion)~Aut(Hlt,(2gi)"(x, C y)) which, being the intersection of a discrete and a compact subgroup of Aut (H,), is finite. As ~o+ Up is clearly a group homomorphism, it remains to prove its kernel is finite. But ~o ~ Up is injective, unless H z = torsion. In the latter case, Aut (Hz) is a finite group. Q.E.D. (4.2.1) Let 5 ~ be a topological space. A family of pure Hodge structures of weight n on 5 e is by defintion a local system H z of Zmodules of finite type, together with a continuously warying filtration F+ i of (Hc)s, the complexification of the stalk of Hz at s, which point by point is a pure Hodge structure of weight n. (4.2.1.1) A polarization of a family of pure Hodge structures of weight n is by definition a morphism of local systems on b ~ (4.2.1.2) (,): Hz...
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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
 NormanKatz

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