R-EQUIVALENCE ON GROUP SCHEMES AND NON STABLE K 1 -FUNCTORS

Authors :: Gille, Philippe
Stavrova, A
Institut Camille Jordan [Villeurbanne] (ICJ)
École Centrale de Lyon (ECL)
Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL)
Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon)
Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)
Chebyshev Laboratory, St. Petersburg State University
Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon)
Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)
Publication Year :: 2021
Publisher :: HAL CCSD, 2021.
Abstract: We define R-equivalence for group schemes over a semilocal ring and relate this with rational properties. Two main cases are investigated: tori and isotropic semisimple simply connected group schemes where we show in certain cases that R-equivalence coincide with Karoubi-Villamayor equivalence and is also related to the Kneser-Tits problem in this setting. Finally we construct specialization maps for R-equivalence in the case of regular algebras containing a field.

Subjects :: resolution property. MSC 2000: 14L15
Group schemes
tori
[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]
representations
20G35
R-equivalence
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
Reductive group schemes
Whitehead groups and K 1
Karoubi-Villamayor Ktheory

Tools