Unformatted text preview: (220.127.116.11) s(z)=multiplication by zP~ q on H p'q. Following Well, we put C = s (i). For each z ~C*, the endomorphism s(z) of H c commutes with complex conjugation, and hence comes from an endomorphism still noted s(z) of Hn= Hz| R denoting the field of real numbers. (18.104.22.168) A morphism q9 between pure Hodge structures H and H' is a group homomorphism ~Oz: Hz---~H'z whose C-linear extension <Pc: Hc--* H~: commutes with the action s of C* (22.214.171.124). (Thus between pure Hodge structure of different weights there is only the zero morphism.) (126.96.36.199) The category of pure Hodge structures has an internal Hom and a tensor product | defined in the expected way (cf. ). (188.8.131.52) Tate's Hodge structure Z(n) is the rank one Hodge structure of weight - 2 n which is purely of type (- n, - n), and whose integral lattice H z is the subgroup (184.108.40.206) (2n i)" Zc C....
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- Fall '11
- Vector Space, Hodge, automorphism, pure Hodge structures