[Remarques sur le complexe de Schweitzer]
Nous prouvons que le complexe de Schweitzer est elliptique et que ses cohomologies définissent des foncteurs cohomologiques. Comme applications, nous obtenons la dimensionnalité finie, une version de la dualité de Serre, des restrictions du comportement de la cohomologie dans les petites déformations, et une formule d’index qui s’avère être équivalente aux relations de Hirzebruch–Riemann–Roch.
We prove that the Schweitzer complex is elliptic and its cohomologies define cohomological functors. As applications, we obtain finite dimensionality, a version of Serre duality, restrictions of the behaviour of cohomology in small deformations, and an index formula which turns out to be equivalent to the Hirzebruch–Riemann–Roch relations.
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Keywords: Complex manifolds, Cohomology, Index theory, Deformations.
Mot clés : Variétés complexes, cohomologie, théorie de l’indice, déformations.
Stelzig, Jonas 1
@unpublished{AIF_0__0_0_A99_0,
author = {Stelzig, Jonas},
title = {Some remarks on the {Schweitzer} complex},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
year = {2024},
doi = {10.5802/aif.3645},
language = {en},
note = {Online first},
}
Stelzig, Jonas. Some remarks on the Schweitzer complex. Annales de l'Institut Fourier, Online first, 13 p.
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