Geodesic
The Grothendieck Trace and the de Rham Integral
Canadian mathematical bulletin, Tome 46 (2003) no. 3, pp. 429-440

Voir la notice de l'article provenant de la source Cambridge University Press

On a smooth $n$ -dimensional complete variety $X$ over $\mathbb{C}$ we show that the trace map ${{\bar{\theta }}_{X}}\,:\,{{H}^{n}}(X,\,\Omega _{X}^{n})\,\to \,\mathbb{C}$ arising from Lipman's version of Grothendieck duality in $\left[ \text{L} \right]$ agrees with $${{(2\pi i)}^{-n}}{{(-1)}^{n(n-1)/2}}\,\int_{X}{:\,H_{DR}^{2n}\,(X,\,\mathbb{C})\,\to \,\mathbb{C}}$$ under the Dolbeault isomorphism.
DOI : 10.4153/CMB-2003-043-3
Mots-clés : 14F10, 32A25, 14A15, 14F05, 18E30 
Sastry, Pramathanath; Tong, Yue Lin L. The Grothendieck Trace and the de Rham Integral. Canadian mathematical bulletin, Tome 46 (2003) no. 3, pp. 429-440. doi: 10.4153/CMB-2003-043-3
@article{10_4153_CMB_2003_043_3,
     author = {Sastry, Pramathanath and Tong, Yue Lin L.},
     title = {The {Grothendieck} {Trace} and the de {Rham} {Integral}},
     journal = {Canadian mathematical bulletin},
     pages = {429--440},
     year = {2003},
     volume = {46},
     number = {3},
     doi = {10.4153/CMB-2003-043-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-043-3/}
}
TY  - JOUR
AU  - Sastry, Pramathanath
AU  - Tong, Yue Lin L.
TI  - The Grothendieck Trace and the de Rham Integral
JO  - Canadian mathematical bulletin
PY  - 2003
SP  - 429
EP  - 440
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-043-3/
DO  - 10.4153/CMB-2003-043-3
ID  - 10_4153_CMB_2003_043_3
ER  - 
%0 Journal Article
%A Sastry, Pramathanath
%A Tong, Yue Lin L.
%T The Grothendieck Trace and the de Rham Integral
%J Canadian mathematical bulletin
%D 2003
%P 429-440
%V 46
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-043-3/
%R 10.4153/CMB-2003-043-3
%F 10_4153_CMB_2003_043_3

[C] [C] Conrad, B., Grothendieck duality and base change. Lecture Notes in Math. 1750, Springer-Verlag, New York, 2000. Google Scholar

[C1] [C1] Conrad, B., Clarifications and corrections to .Grothendieck duality and base change.. Preprint, www-math.mit.edu/.dejong. Google Scholar

[C2] [C2] Conrad, B., More Examples. Preprint, www-math.mit.edu/.dejong. Google Scholar

[D] [D] Deligne, P., Intégration sur un cycle évanescent. Invent.Math. 76 (1983), 129–143. Google Scholar

[dR] [dR] de Rham, G., Variétés différentiables. Hermann, Paris, 1955. Google Scholar

[GH] [GH] Griffiths, P. and Harris, J., Principles of Algebraic Geometry. John Wiley & Sons, New York, 1978. Google Scholar

[G1] [G1] Grothendieck, A., Théorèmes de dualité pour les faisceaux algébriques cohérents. Séminaire Bourbaki 149, May 1957. Google Scholar

[G2] [G2] Grothendieck, A., Rev.etements étales et groupe fondamental. Lecture Notes in Math. 224, Springer-Verlag, Heidelberg, 1971. Google Scholar

[Ha] [Ha] Hartshorne, R., Algebraic Geometry. Graduate Texts in Math. 52, Springer-Verlag, 1977. Google Scholar

[H] [H] Harvey, F. R., Integral formulae connected by Dolbeault's isomorphism. Rice Univ. Studies 56 (1970), 77–97. Google Scholar

[I] [I] Iversen, B., Cohomology of sheaves. Universitext, Springer-Verlag, 1986. Google Scholar

[L] [L] Lipman, J., Dualizing sheaves, differentials and residues on algebraic varieties. Astérisque 117, 1984. Google Scholar

[T] [T] Tong, Y. L. L., Integral representation formulae and the Grothendieck residue symbol. Amer. J. Math. 95 (1973), 904–917. Google Scholar

[TT] [TT] Toledo, D. and Tong, Y. L. L., A parametrix for ∂ and the Riemann-Roch in Čech theory. Topology 15 (1976), 273–301. Google Scholar

Cité par Sources :