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

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DOI

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
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     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/}
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