A weak GAGA statement for arbitrary morphisms
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- by Amnon Neeman PDF
- Proc. Amer. Math. Soc. 100 (1987), 429-432 Request permission
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
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A. Neeman, GAGA for quotient varieties (to appear).
- Jean-Pierre Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier (Grenoble) 6 (1955/56), 1–42 (French). MR 82175
- Gerald W. Schwarz, Lifting smooth homotopies of orbit spaces, Inst. Hautes Études Sci. Publ. Math. 51 (1980), 37–135. MR 573821
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 429-432
- MSC: Primary 32C35; Secondary 14F05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0891140-5
- MathSciNet review: 891140