Virtual pullbacks in K-theory  [ Tirés en arrière virtuels en K-théorie ]
Annales de l'Institut Fourier, Tome 68 (2018) no. 4, p. 1609-1641
Nous considérons les tirés en arrière virtuels en K-théorie, et montrons qu’ils sont des classes bivariantes et satisfaisant une certaine forme de fonctorialité. En tant qu’applications aux invariants de comptage K-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 K-theory, and show that they are bivariant classes and satisfy certain functoriality. As applications to K-theoretic counting invariants, we include proofs of a virtual localization formula for schemes and a degeneration formula in Donaldson–Thomas theory.
Reçu le : 2016-11-12
Accepté le : 2017-09-14
Publié le : 2018-11-23
DOI : https://doi.org/10.5802/aif.3194
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 $K$-theory},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {4},
     year = {2018},
     pages = {1609-1641},
     doi = {10.5802/aif.3194},
     language = {en},
     url = {https://aif.centre-mersenne.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. https://aif.centre-mersenne.org/item/AIF_2018__68_4_1609_0/

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