J -invariant of linear algebraic groups

Viktor Petrov; Nikita Semenov; Kirill Zainoulline

Annales scientifiques de l'École Normale Supérieure (2008)

  • Volume: 41, Issue: 6, page 1023-1053
  • ISSN: 0012-9593

Abstract

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Let G be a semisimple linear algebraic group of inner type over a field F , and let X be a projective homogeneous G -variety such that G splits over the function field of X . We introduce the J -invariant of G which characterizes the motivic behavior of X , and generalizes the J -invariant defined by A. Vishik in the context of quadratic forms. We use this J -invariant to provide motivic decompositions of all generically split projective homogeneous G -varieties, e.g. Severi-Brauer varieties, Pfister quadrics, maximal orthogonal Grassmannians, varieties of Borel subgroups of G . We also discuss relations with torsion indices, canonical dimensions and cohomological invariants of the group G .

How to cite

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Petrov, Viktor, Semenov, Nikita, and Zainoulline, Kirill. "$J$-invariant of linear algebraic groups." Annales scientifiques de l'École Normale Supérieure 41.6 (2008): 1023-1053. <http://eudml.org/doc/272139>.

@article{Petrov2008,
abstract = {Let $G$ be a semisimple linear algebraic group of inner type over a field $F$, and let $X$ be a projective homogeneous $G$-variety such that $G$ splits over the function field of $X$. We introduce the $J$-invariant of $G$ which characterizes the motivic behavior of $X$, and generalizes the $J$-invariant defined by A. Vishik in the context of quadratic forms. We use this $J$-invariant to provide motivic decompositions of all generically split projective homogeneous $G$-varieties, e.g. Severi-Brauer varieties, Pfister quadrics, maximal orthogonal Grassmannians, varieties of Borel subgroups of $G$. We also discuss relations with torsion indices, canonical dimensions and cohomological invariants of the group $G$.},
author = {Petrov, Viktor, Semenov, Nikita, Zainoulline, Kirill},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {motive; algebraic group; homogeneous variety},
language = {eng},
number = {6},
pages = {1023-1053},
publisher = {Société mathématique de France},
title = {$J$-invariant of linear algebraic groups},
url = {http://eudml.org/doc/272139},
volume = {41},
year = {2008},
}

TY - JOUR
AU - Petrov, Viktor
AU - Semenov, Nikita
AU - Zainoulline, Kirill
TI - $J$-invariant of linear algebraic groups
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2008
PB - Société mathématique de France
VL - 41
IS - 6
SP - 1023
EP - 1053
AB - Let $G$ be a semisimple linear algebraic group of inner type over a field $F$, and let $X$ be a projective homogeneous $G$-variety such that $G$ splits over the function field of $X$. We introduce the $J$-invariant of $G$ which characterizes the motivic behavior of $X$, and generalizes the $J$-invariant defined by A. Vishik in the context of quadratic forms. We use this $J$-invariant to provide motivic decompositions of all generically split projective homogeneous $G$-varieties, e.g. Severi-Brauer varieties, Pfister quadrics, maximal orthogonal Grassmannians, varieties of Borel subgroups of $G$. We also discuss relations with torsion indices, canonical dimensions and cohomological invariants of the group $G$.
LA - eng
KW - motive; algebraic group; homogeneous variety
UR - http://eudml.org/doc/272139
ER -

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