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Cohomology of projective space seen by residual complex
Author(s):
I-Chiau
Huang
Journal:
Trans. Amer. Math. Soc.
353
(2001),
3097-3114.
MSC (2000):
Primary 14F05, 14F10;
Secondary 13N05
Posted:
March 12, 2001
MathSciNet review:
1828600
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Abstract:
A subcomplex of a residual complex on projective space is constructed for computing the cohomology modules of locally free sheaves. A constructive new proof of the Bott formula is given by explicitly exhibiting bases for the cohomology modules.
References:
-
- 1.
- R. Bott.
Homogeneous vector bundles.
Annals of Math., 66:203-248, 1957. MR 19:681d - 2.
- A. Grothendieck.
The cohomology theory of abstract algebraic varieties.
In Proc. Internat. Congress Math. (Edinburgh, 1958), pages 103-118. Cambridge University Press, 1960. MR 24:A733 - 3.
- R. Hartshorne.
Residues and Duality, volume 20 of Lecture Notes in Mathematics.
Springer-Verlag, 1966. MR 36:5145 - 4.
- R. Hartshorne.
Algebraic Geometry.
Springer-Verlag, 1977. MR 57:3116 - 5.
- I-C. Huang.
An explicit construction of residual complexes.
Journal of Algebra, 225:698-739, 2000. CMP 2000:09 - 6.
- I-C. Huang.
Pseudofunctors on modules with zero-dimensional support.
Mem. Amer. Math. Soc., 114(no. 548):xii+53, 1995. MR 95h:13013 - 7.
- I-C. Huang.
A residue map and its applications to some one-dimensional rings.
Proc. Amer. Math. Soc., 123(8):2369-2372, 1995. MR 95j:13019 - 8.
- I-C. Huang.
Residue theorem via an explicit construction of traces.
preprint, 1996. - 9.
- I-C. Huang.
Theory of residues on the projective plane.
Manuscripta Math., 92(2):259-272, 1997. MR 98a:14027 - 10.
- R. Hübl.
Residues of regular and meromorphic differential forms.
Math. Ann., 300(4):605-628, 1994. MR 96e:14017 - 11.
- J. Lipman and P. Sastry.
Residues and duality for Cousin complexes.
preprint, September 21, 1996. - 12.
- P. Sastry.
Residues and duality for algebraic schemes.
Compositio Math., 101(2):133-178, 1996. MR 98a:14029 - 13.
- P. Sastry and A. Yekutieli.
On residue complexes, dualizing sheaves and local cohomology modules.
Israel J. Math., 90:325-348, 1995. MR 96f:14021 - 14.
- A. Yekutieli.
An explicit construction of the Grothendieck residue complex.
Astérisque 208, 1992.
With an appendix by Pramathanath Sastry. MR 94e:14026 - 15.
- A. Yekutieli.
Residues and differential operators on schemes.
Duke Math. J., 95(2):305-341, 1998. MR 99j:14019 - 16.
- A. Yekutieli.
Smooth formal embeddings and the residue complex.
Canad. J. Math., 50(4):863-896, 1998. MR 99i:14004
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Additional Information:
I-Chiau
Huang
Affiliation:
Institute of Mathematics, Academia Sinica, Nankang, Taipei 11529, Taiwan, R.O.C.
Email:
ichuang@math.sinica.edu.tw
DOI:
10.1090/S0002-9947-01-02686-1
PII:
S 0002-9947(01)02686-1
Keywords:
Bott formula,
injective resolution,
residual complex
Received by editor(s):
January 10, 2000
Posted:
March 12, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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