Nous considérons les tirés en arrière virtuels en -théorie, et montrons qu’ils sont des classes bivariantes et satisfaisant une certaine forme de fonctorialité. En tant qu’applications aux invariants de comptage -théoriques, nous incluons des preuves d’une formule de localisation virtuelle pour les schémas et une formule de dégénérescence en théorie de Donaldson–Thomas.
We consider virtual pullbacks in -theory, and show that they are bivariant classes and satisfy certain functoriality. As applications to -theoretic counting invariants, we include proofs of a virtual localization formula for schemes and a degeneration formula in Donaldson–Thomas theory.
Accepté le : 2017-09-13
Publié le : 2018-11-22
Classification : 14C17, 14A20, 14C35, 14N35
Mots clés : tiré en arrière virtuel, localisation virtuelle, formule de dégénérescence
@article{AIF_2018__68_4_1609_0,
author = {Qu, Feng},
title = {Virtual pullbacks in <span class="mathjax-formula">$K$</span>-theory},
journal = {Annales de l'Institut Fourier},
pages = {1609--1641},
publisher = {Association des Annales de l'institut Fourier},
volume = {68},
number = {4},
year = {2018},
doi = {10.5802/aif.3194},
language = {en},
url = {archive.numdam.org/item/AIF_2018__68_4_1609_0/}
}
Qu, Feng. Virtual pullbacks in $K$-theory. Annales de l'Institut Fourier, Tome 68 (2018) no. 4, pp. 1609-1641. doi : 10.5802/aif.3194. http://archive.numdam.org/item/AIF_2018__68_4_1609_0/
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