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.
- 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
- I-Chiau Huang
- Affiliation: Institute of Mathematics, Academia Sinica, Nankang, Taipei 11529, Taiwan, R.O.C.
- Email: email@example.com
- 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