Geodesic
Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior
Documenta mathematica, Tome 26 (2021), pp. 523-536

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We show that Chow groups of low dimension cycles are torsion free for a class of sufficiently generic Severi-Brauer varieties. Using a recent result of Karpenko, this allows us to compute the algebraic connective K-theory in low degrees for the same class of varieties. Independently of these results, we show that the associated graded ring for the topological filtration on the Grothendieck ring is torsion free in the same degrees for an arbitrary Severi-Brauer variety.
DOI : 10.4171/dm/820
Classification : 14C25, 14C35, 19L41
Mots-clés : Severi-Brauer varieties, algebraic connective K-theory 
Eoin Mackall. Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior. Documenta mathematica, Tome 26 (2021), pp. 523-536. doi: 10.4171/dm/820
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     author = {Eoin Mackall},
     title = {Algebraic connective $K$-theory of a {Severi-Brauer} variety with prescribed reduced behavior},
     journal = {Documenta mathematica},
     pages = {523--536},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/820},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/820/}
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