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Correction to the paper ``Duality and flat base change on formal schemes''
Author(s):
Leovigildo
Alonso
Tarrío;
Ana
Jeremías
López;
Joseph
Lipman
Journal:
Proc. Amer. Math. Soc.
131
(2003),
351-357.
MSC (2000):
Primary 14F99;
Secondary 13D99, 14B15, 32C37
Posted:
June 5, 2002
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Abstract:
In §8.3 of our paper ``Duality and Flat Base Change on Formal Schemes" some important results concerning localization and preservation of coherence by basic duality functors were based on the false statement that any closed formal subscheme of an open subscheme of the completion  of a relative projective space is an open subscheme of a closed formal subscheme of  . In this note, the said results are provided with solid foundations.
References:
-
- [DFS]
- L.Alonso Tarrío, A.Jeremías López, J. Lipman, Duality and flat base change on formal schemes. Studies in duality on Noetherian formal schemes and non-Noetherian ordinary schemes, Contemporary Mathematics, 244, American Mathematical Soc., Providence, RI, 1999, 3-90.MR 2000h:14017
- [Co]
- B.Conrad, Deligne's notes on Nagata Compactifications, item 5 on <http://www-math. mit.edu/~dejong/#brian>
- [De]
- P.Deligne, Cohomologie à supports propres. Théorie des Topos et cohomologie Étale des Schémas (SGA4) Tome 3, Lecture Notes in Math. no. 305, Springer-Verlag, New York, 1973, 250-461. MR 50:7132
- [Ha]
- R. Hartshorne, Residues and Duality, Lecture Notes in Math., no.20, Springer-Verlag, New York, 1966. MR 36:5145
- [HR]
- W.Heinzer and C.Rotthaus, Formal fibers and complete homomorphic images, Proc. Amer. Math. Soc. 120 (1994), 359-369.MR 94d:13020
- [Li]
- J. Lipman, Non-noetherian Grothendieck duality. Studies in duality on Noetherian formal schemes and non-Noetherian ordinary schemes, Contemporary Mathematics, 244, American Mathematical Soc., Providence, RI, 1999, 115-123.MR 2000h:14017
- [Lü]
- W. Lütkebohmert, On compactification of schemes, Manuscr. Math. 80, (1993), 95-111.MR 94h:14004
- [Ne]
- A. Neeman, The Grothendieck duality theorem via Bousfield's techniques and Brown representability, J. Amer. Math. Soc. 9 (1996), 205-236.MR 96c:18006
- [Ve]
- J.L.Verdier, Base change for twisted inverse image of coherent sheaves. Algebraic Geometry, Oxford Univ. Press, 1969, 393-408.MR 43:227
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Additional Information:
Leovigildo
Alonso
Tarrío
Affiliation:
Departamento de Álxebra, Facultade de Matemáticas, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain
Email:
leoalonso@usc.es
Ana
Jeremías
López
Affiliation:
Departamento de Álxebra, Facultade de Matemáticas, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain
Email:
jeremias@usc.es
Joseph
Lipman
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
lipman@math.purdue.edu
DOI:
10.1090/S0002-9939-02-06558-9
PII:
S 0002-9939(02)06558-9
Keywords:
Grothendieck duality,
formal scheme
Received by editor(s):
July 2, 2001
Received by editor(s) in revised form:
September 7, 2001
Posted:
June 5, 2002
Additional Notes:
The first two authors were partially supported by Spain's DGESIC PB97-0530 research project. They thank the Mathematics Department of Purdue University for its hospitality and support.
The third author was partially supported by the National Security Agency.
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
2002,
American Mathematical Society
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