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.
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.
Accepted:
Published online:
Keywords: virtual pullback, virtual localization, degeneration formula
Mot 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}, pages = {1609--1641}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {4}, year = {2018}, doi = {10.5802/aif.3194}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.3194/} }
TY - JOUR AU - Qu, Feng TI - Virtual pullbacks in $K$-theory JO - Annales de l'Institut Fourier PY - 2018 SP - 1609 EP - 1641 VL - 68 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3194/ DO - 10.5802/aif.3194 LA - en ID - AIF_2018__68_4_1609_0 ER -
Qu, Feng. Virtual pullbacks in $K$-theory. Annales de l'Institut Fourier, Volume 68 (2018) no. 4, pp. 1609-1641. doi : 10.5802/aif.3194. http://archive.numdam.org/articles/10.5802/aif.3194/
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