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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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