## Cohomology of projective space seen by residual complex

HTML articles powered by AMS MathViewer

- by I-Chiau Huang PDF
- Trans. Amer. Math. Soc.
**353**(2001), 3097-3114 Request permission

## 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

- Saunders MacLane and O. F. G. Schilling,
*Infinite number fields with Noether ideal theories*, Amer. J. Math.**61**(1939), 771–782. MR**19**, DOI 10.2307/2371335 - Alexander Grothendieck,
*The cohomology theory of abstract algebraic varieties*, Proc. Internat. Congress Math. 1958., Cambridge Univ. Press, New York, 1960, pp. 103–118. MR**0130879** - Robin Hartshorne,
*Residues and duality*, Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin-New York, 1966. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64; With an appendix by P. Deligne. MR**0222093** - Robin Hartshorne,
*Algebraic geometry*, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR**0463157** - I-C. Huang. An explicit construction of residual complexes.
*Journal of Algebra*, 225:698–739, 2000. - I-Chiau Huang,
*Pseudofunctors on modules with zero-dimensional support*, Mem. Amer. Math. Soc.**114**(1995), no. 548, xii+53. MR**1239604**, DOI 10.1090/memo/0548 - I-Chiau Huang,
*A residue map and its applications to some one-dimensional rings*, Proc. Amer. Math. Soc.**123**(1995), no. 8, 2369–2372. MR**1254843**, DOI 10.1090/S0002-9939-1995-1254843-3 - I-C. Huang. Residue theorem via an explicit construction of traces. preprint, 1996.
- I-Chiau Huang,
*Theory of residues on the projective plane*, Manuscripta Math.**92**(1997), no. 2, 259–272. MR**1428652**, DOI 10.1007/BF02678193 - Reinhold Hübl,
*Residues of regular and meromorphic differential forms*, Math. Ann.**300**(1994), no. 4, 605–628. MR**1314737**, DOI 10.1007/BF01450504 - J. Lipman and P. Sastry. Residues and duality for Cousin complexes. preprint, September 21, 1996.
- Pramathanath Sastry,
*Residues and duality for algebraic schemes*, Compositio Math.**101**(1996), no. 2, 133–178. MR**1389365** - Pramathanath Sastry and Amnon Yekutieli,
*On residue complexes, dualizing sheaves and local cohomology modules*, Israel J. Math.**90**(1995), no. 1-3, 325–348. MR**1336329**, DOI 10.1007/BF02783219 - Amnon Yekutieli,
*An explicit construction of the Grothendieck residue complex*, Astérisque**208**(1992), 127 (English, with French summary). With an appendix by Pramathanath Sastry. MR**1213064** - Amnon Yekutieli,
*Residues and differential operators on schemes*, Duke Math. J.**95**(1998), no. 2, 305–341. MR**1652013**, DOI 10.1215/S0012-7094-98-09509-6 - Amnon Yekutieli,
*Smooth formal embeddings and the residue complex*, Canad. J. Math.**50**(1998), no. 4, 863–896. MR**1638635**, DOI 10.4153/CJM-1998-046-1

## Additional Information

**I-Chiau Huang**- Affiliation: Institute of Mathematics, Academia Sinica, Nankang, Taipei 11529, Taiwan, R.O.C.
- Email: ichuang@math.sinica.edu.tw
- Received by editor(s): January 10, 2000
- Published electronically: March 12, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**353**(2001), 3097-3114 - MSC (2000): Primary 14F05, 14F10; Secondary 13N05
- DOI: https://doi.org/10.1090/S0002-9947-01-02686-1
- MathSciNet review: 1828600