Representability of Hom implies flatness
نویسندگان
چکیده
منابع مشابه
A ug 2 00 3 Representability of Hom implies flatness
Let X be a projective scheme over a noetherian base scheme S, and let F be a coherent sheaf on X. For any coherent sheaf E on X, consider the set-valued contravariant functor Hom(E,F) on S-schemes, defined by Hom(E,F)(T ) = Hom(ET ,FT ) where ET and FT are the pull-backs of E and F to XT = X ×S T . A basic result of Grothendieck ([EGA] III 7.7.8, 7.7.9) says that if F is flat over S then Hom(E,...
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ژورنال
عنوان ژورنال: Proceedings Mathematical Sciences
سال: 2004
ISSN: 0253-4142,0973-7685
DOI: 10.1007/bf02829667