Journal of Algebraic Geometry

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Finiteness of coherent cohomology for proper $\text{fppf}$ stacks

Author(s): Gerd Faltings
Journal: J. Algebraic Geom. 12 (2003), 357-366.
Posted: September 18, 2002
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Abstract | References | Additional information

Abstract: We prove the result in the title for Noetherian fppf stacks, avoiding the use of Chow's lemma. Instead we employ simplicial schemes and shrinking-methods.

References:

1.: L.Gruson, M.Raynaud, Critères de platitude et de projectivité, Inv. math. 13(1971), 1-89
2.: R.Kiehl, Theorem A und Theorem B in der nichtarchimedischen Funktionentheorie, Inv. math. 2(1967), 256-273
3.: G.Laumon, L.Moret-Bailly, Champs algébriques, Springer-Verlag, Berlin, 2000

Additional Information:

Gerd Faltings
Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
Email: gerd@mpim-bonn.mpg.de

PII: S 1056-3911(02)00321-1
Received by editor(s): November 2, 2000
Posted: September 18, 2002

The Journal of Algebraic Geometry
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