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Proceedings of the American Mathematical Society

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A weak GAGA statement for arbitrary morphisms

Author: Amnon Neeman
Journal: Proc. Amer. Math. Soc. 100 (1987), 429-432
MSC: Primary 32C35; Secondary 14F05
MathSciNet review: 891140
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Abstract: Let $ f:X \to Y$ be an arbitrary morphism of schemes of finite type over $ {\mathbf{C}}$, and let $ {f^{{\text{an}}}}$ be the associated map of analytic spaces. Let $ \mathcal{S}$ be a coherent sheaf on $ X$. Then $ {({f_*}\mathcal{S})^{{\text{an}}}} \to f_*^{{\text{an}}}({\mathcal{S}^{{\text{an}}}})$ is injective.

References [Enhancements On Off] (What's this?)

  • [N] A. Neeman, GAGA for quotient varieties (to appear).
  • [GAGA] Jean-Pierre Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, Grenoble 6 (1955–1956), 1–42 (French). MR 0082175
  • [S] Gerald W. Schwarz, Lifting smooth homotopies of orbit spaces, Inst. Hautes Études Sci. Publ. Math. 51 (1980), 37–135. MR 573821

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Article copyright: © Copyright 1987 American Mathematical Society

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