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The Grothendieck Trace and the de Rham Integral

  Published:2003-09-01
 Printed: Sep 2003
  • Pramathanath Sastry
  • Yue Lin L. Tong
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Abstract

On a smooth $n$-dimensional complete variety $X$ over ${\mathbb C}$ we show that the trace map ${\tilde\theta}_X \colon\break H^n (X,\Omega_X^n) \to {\mathbb C}$ arising from Lipman's version of Grothendieck duality in \cite{ast-117} agrees with $$ (2\pi i)^{-n} (-1)^{n(n-1)/2} \int_X \colon H^{2n}_{DR} (X,{\mathbb C}) \to {\mathbb C} $$ under the Dolbeault isomorphism.
MSC Classifications: 14F10, 32A25, 14A15, 14F05, 18E30 show english descriptions Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]
Integral representations; canonical kernels (Szegoo, Bergman, etc.)
Schemes and morphisms
Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Derived categories, triangulated categories
14F10 - Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]
32A25 - Integral representations; canonical kernels (Szegoo, Bergman, etc.)
14A15 - Schemes and morphisms
14F05 - Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
18E30 - Derived categories, triangulated categories
 

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