Geodesic
On the Chow ring of the classifying stack of algebraic tori
Documenta mathematica, Tome 27 (2022), pp. 917-932

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We investigate the structure of the Chow ring of the classifying stacks BT 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 AT2​ in the general case. Building on this work, Scavia exhibited an example where (AT2​)tors​=0.
DOI : 10.4171/dm/888
Classification : 14A20, 14C15, 14C17
Mots-clés : torsors, Chow ring, torsion classes, classifying stack 
Francesco Sala. On the Chow ring of the classifying stack of algebraic tori. Documenta mathematica, Tome 27 (2022), pp. 917-932. doi: 10.4171/dm/888
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     author = {Francesco Sala},
     title = {On the {Chow} ring of the classifying stack of algebraic tori},
     journal = {Documenta mathematica},
     pages = {917--932},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/888},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/888/}
}
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