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Problems in R-equivalence of semisimple groups

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Abstract

R-equivalence on the unimodular group of a simple algebra is studied in detail. A rather complete characterization is obtained for the R-equivalence group of semisimple groups over the field of

-adic numbers. In this case all the Manin groups are commutative, and for simply connected groups, they are trivial. It is shown how R-equivalence can be applied to the weak approximation problem.

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Authors
  1. V. E. Voskresenskii
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Additional information

Translated from Zapiskii Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 86, pp. 49–65, 1979.

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Voskresenskii, V.E. Problems in R-equivalence of semisimple groups. J Math Sci 17, 1975–1987 (1981). https://doi.org/10.1007/BF01465455

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