Comptes Rendus
Géométrie algébrique
Motivic classes and the integral Hodge Question
Federico Scavia1
1 Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
Comptes Rendus. Mathématique, Volume 359 (2021) no. 3, pp. 305-311.

We prove that the obstruction to the integral Hodge Question factors through the completion of the Grothendieck ring of varieties for the dimension filtration. As an application, combining work of Peyre, Colliot-Thélène and Voisin, we give the first example of a finite group G such that the motivic class of its classifying stack BG in Ekedahl’s Grothendieck ring of stacks over ℂ is non-trivial and BG has trivial unramified Brauer group.

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DOI : 10.5802/crmath.178
Federico Scavia 1

1 Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Federico Scavia},
     title = {Motivic classes and the integral {Hodge} {Question}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {305--311},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {3},
     year = {2021},
     doi = {10.5802/crmath.178},
     language = {en},
}
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Federico Scavia. Motivic classes and the integral Hodge Question. Comptes Rendus. Mathématique, Volume 359 (2021) no. 3, pp. 305-311. doi : 10.5802/crmath.178. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.178/

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