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Residue: A Geometric Construction

Published online by Cambridge University Press:  20 November 2018

Fernando Sancho de Salas
Fernando Sancho de Salas*
Affiliation:
Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1–4, 37008 Salamanca, Spain, e-mail: [email protected]
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Abstract

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A new construction of the ordinary residue of differential forms is given. This construction is intrinsic, i.e., it is defined without local coordinates, and it is geometric: it is constructed out of the geometric structure of the local and global cohomology groups of the differentials. The Residue Theorem and the local calculation then follow from geometric reasons.

Keywords

14A25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 2 , 01 June 2002 , pp. 284 - 293
Copyright
Copyright © Canadian Mathematical Society 2002

References

[Gro1] Grothendieck, A., Théorèmes de dualité pour les faisceaux algébriques cohérents. Seminaire Bourbaki 149, Secre.Math. I.H.P. Paris, 1957.Google Scholar
[Gro2] Grothendieck, A., Local Cohomology. Lecture Notes in Math. 41, Springer-Verlag, 1967.Google Scholar
[Ha] Hartshorne, R., Residues and Duality. Lecture Notes in Math. 20, Springer-Verlag, 1966.Google Scholar
[HK] Hubl, R. and Kunz, E., Integration of Differential Forms on Schemes. J. Reine Angew. Math 410 (1990), 410–1990.Google Scholar
[Hu] Hubl, R., Traces of Differential Forms and Hochschild Homology. Lecture Notes in Math. 1368, Springer-Verlag, 1989.Google Scholar
[Li1] Lipman, J., Dualizing sheaves, differentials and residues on algebraic varieties. Astérisque 117, 1984.Google Scholar
[Li2] Lipman, J., Residues and Traces of Differential Forms via Hochschild Homology. Contemp. Math. 61, Amer. Math. Soc., Providence, RI, 1987.Google Scholar
[Ma] Matlis, E., Injective modules for noetherian rings. Pacific J. Math. 8 (1958), 8–1958.Google Scholar
[Ta] Tate, J., Residues of differentials on curves. Ann. Sci. École Norm. Sup. (4) 1 (1968), 1–1968.Google Scholar
[Se] Serre, J. P., Groupes Algébriques et Corps de Classes. Hermann, Paris, 1959.Google Scholar