Products of Brauer-Severi surfaces
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- by Amit Hogadi
- Proc. Amer. Math. Soc. 137 (2009), 45-50
- DOI: https://doi.org/10.1090/S0002-9939-08-09450-1
- Published electronically: July 25, 2008
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Abstract:
Let $\{P_i\}_{1 \leq i \leq r}$ and $\{Q_i\}_{1 \leq i \leq r}$ be two collections of Brauer-Severi surfaces (resp. conics) over a field $k$. We show that the subgroup generated by the $P_i$’s in $Br(k)$ is the same as the subgroup generated by the $Q_i$’s if and only if $\prod P_i$ is birational to $\prod Q_i$. Moreover in this case $\prod P_i$ and $\prod Q_i$ represent the same class in $M(k)$, the Grothendieck ring of $k$-varieties. The converse holds if $\mathrm {char}(k)=0$. Some of the above implications also hold over a general noetherian base scheme.References
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Bibliographic Information
- Amit Hogadi
- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- Address at time of publication: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
- Email: amit@math.princeton.edu, amit@math.tifr.res.in
- Received by editor(s): December 29, 2006
- Received by editor(s) in revised form: June 23, 2007, and November 30, 2007
- Published electronically: July 25, 2008
- Communicated by: Ted Chinburg
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 45-50
- MSC (2000): Primary 14E05, 14M99; Secondary 14J25
- DOI: https://doi.org/10.1090/S0002-9939-08-09450-1
- MathSciNet review: 2439423