Proof of Nadel’s conjecture and direct image for relative K -theory

Alain Berthomieu

Bulletin de la Société Mathématique de France (2002)

  • Volume: 130, Issue: 2, page 253-307
  • ISSN: 0037-9484

Abstract

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A “relative” K -theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.

How to cite

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Berthomieu, Alain. "Proof of Nadel’s conjecture and direct image for relative $K$-theory." Bulletin de la Société Mathématique de France 130.2 (2002): 253-307. <http://eudml.org/doc/272417>.

@article{Berthomieu2002,
abstract = {A “relative” $K$-theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.},
author = {Berthomieu, Alain},
journal = {Bulletin de la Société Mathématique de France},
keywords = {relative $K$-theory; holomorphic bundles; characteristic classes; Hodge-Deligne cohomology; Chern-Simons forms; Riemann-Roch theorem},
language = {eng},
number = {2},
pages = {253-307},
publisher = {Société mathématique de France},
title = {Proof of Nadel’s conjecture and direct image for relative $K$-theory},
url = {http://eudml.org/doc/272417},
volume = {130},
year = {2002},
}

TY - JOUR
AU - Berthomieu, Alain
TI - Proof of Nadel’s conjecture and direct image for relative $K$-theory
JO - Bulletin de la Société Mathématique de France
PY - 2002
PB - Société mathématique de France
VL - 130
IS - 2
SP - 253
EP - 307
AB - A “relative” $K$-theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.
LA - eng
KW - relative $K$-theory; holomorphic bundles; characteristic classes; Hodge-Deligne cohomology; Chern-Simons forms; Riemann-Roch theorem
UR - http://eudml.org/doc/272417
ER -

References

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