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II.1.15

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This problems has Hartshorne Height 1.

HAPPY

  • The key to this problem is to reduce statements of morphisms of sheaves to statements about elements of sheaf groups.
    • Defining the sum of two morphisms is just defined pointwise on every open set as you would expect.
    • In particular, the zero and gluing sheaf axioms for Hom(F|_U,G|_U) (here the underline means sheaf Hom) only require that G be a sheaf. For example, for the zero axiom, if a morphism restricts to 0 on some open cover means that the original morhpism maps elements to other elements that restricts to 0 in the groups of G, as G is a sheaf, the morphism must be mapping everything to 0.

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