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Adjoint groups over $ {\mathbb{Q}}_p (X)$ and R-equivalence - revisited


Authors: R. Preeti and A. Soman
Journal: Proc. Amer. Math. Soc. 145 (2017), 1019-1029
MSC (2010): Primary 11Sxx; Secondary 20G99
DOI: https://doi.org/10.1090/proc/13304
Published electronically: September 15, 2016
MathSciNet review: 3589302
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Abstract: We obtain a class of examples of non-rational adjoint classical groups of type $ ^2A_n$ and a group of type $ ^2D_3$ over the function field $ F$ of a smooth geometrically integral curve over a $ p$-adic field with $ p \neq 2$. We also show that for any group of type $ C_n$ over $ F$, the group of rational equivalence classes of $ G$ over $ F$ is trivial, i.e., $ G(F)/R=(1)$.


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Additional Information

R. Preeti
Affiliation: Department of Mathematics, Indian Institute of Technology (Bombay), Powai, Mumbai-400076, India
Email: preeti@math.iitb.ac.in

A. Soman
Affiliation: Department of Mathematical Sciences, Indian Institute of Science Education and Research, Mohali, Sector 81, SAS Nagar, Manauli, Punjab-140306, India
Email: somanabhay@iisermohali.ac.in

DOI: https://doi.org/10.1090/proc/13304
Received by editor(s): April 30, 2016
Received by editor(s) in revised form: May 12, 2016
Published electronically: September 15, 2016
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society

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