Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

$R$-equivalence in adjoint classical groups over fields of virtual cohomological dimension $2$
HTML articles powered by AMS MathViewer

by Amit Kulshrestha and R. Parimala PDF
Trans. Amer. Math. Soc. 360 (2008), 1193-1221 Request permission

Abstract:

Let $F$ be a field of characteristic not $2$ whose virtual cohomological dimension is at most $2$. Let $G$ be a semisimple group of adjoint type defined over $F$. Let $RG(F)$ denote the normal subgroup of $G(F)$ consisting of elements $R$-equivalent to identity. We show that if $G$ is of classical type not containing a factor of type $D_n$, $G(F)/RG(F) = 0$. If $G$ is a simple classical adjoint group of type $D_n$, we show that if $F$ and its multi-quadratic extensions satisfy strong approximation property, then $G(F)/RG(F) = 0$. This leads to a new proof of the $R$-triviality of $F$-rational points of adjoint classical groups defined over number fields.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20G15, 14G05
  • Retrieve articles in all journals with MSC (2000): 20G15, 14G05
Additional Information
  • Amit Kulshrestha
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, India 400005
  • Email: amitk@math.tifr.res.in
  • R. Parimala
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, India 400005
  • Address at time of publication: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
  • MR Author ID: 136195
  • Email: parimala@mathcs.emory.edu
  • Received by editor(s): July 31, 2005
  • Published electronically: October 23, 2007

  • Dedicated: Dedicated to our teacher Professor R. Sridharan on his seventieth birthday.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 1193-1221
  • MSC (2000): Primary 20G15, 14G05
  • DOI: https://doi.org/10.1090/S0002-9947-07-04300-0
  • MathSciNet review: 2357694