On the Chow ring of the classifying stack of algebraic tori
Francesco SalaScuola Normale Superiore, Piazza dei cavalieri 7, 56126 Pisa, Italy
We investigate the structure of the Chow ring of the classifying stacks of algebraic tori, as it has been defined by B. Totaro. Some previous work of N. Karpenko, A. Merkurjev, S. Blinstein and F. Scavia has shed some light on the structure of such rings. In particular Karpenko showed the absence of torsion classes in the case of permutation tori, while Merkurjev and Blinstein described in a very effective way the second equivariant Chow group in the general case. Building on this work, Scavia exhibited an example where .
Here, by making use of a very elementary approach, we extend the result of Karpenko to special tori and we completely determine the Chow ring when is an algebraic torus admitting a resolution with special tori . In particular we show that there can be torsion in the Chow ring of such tori.
Cite this article
Francesco Sala, On the Chow ring of the classifying stack of algebraic tori. Doc. Math. 27 (2022), pp. 917–932DOI 10.4171/DM/888