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Jul 12 at 12:54 comment added Daniel Litt @Dr.Evil This follows from the last clause in the statement of the theorem. An isomorphism of vector spaces which respects Hodge structures is an isomorphism of Hodge structures.
Jul 12 at 10:30 comment added Dr. Evil Why does the second paragraph follow from the first? I understand all fibres must have isomorphic cohomology if the base is simply connected. But why must the map $H^0(S,V)\rightarrow V_s$ be an isomorphism of Hodge Structures?
Sep 15, 2017 at 4:18 vote accept asv
Sep 14, 2017 at 23:14 history answered Daniel Litt CC BY-SA 3.0