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Transactions of the American Mathematical Society

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

 
 

 

Chow groups of products of Severi-Brauer varieties and invariants of degree $ 3$


Author: Sanghoon Baek
Journal: Trans. Amer. Math. Soc. 369 (2017), 1757-1771
MSC (2010): Primary 11E72, 14F43, 14M17, 20G15
DOI: https://doi.org/10.1090/tran/6772
Published electronically: May 3, 2016
MathSciNet review: 3581218
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Abstract: We study the semi-decomposable invariants of a split semisimple group and their extension to a split reductive group by using the torsion in the codimension $ 2$ Chow groups of a product of Severi-Brauer varieties. In particular, for any $ n\geq 2$ we completely determine the degree $ 3$ invariants of a split semisimple group, the quotient of $ (\mathbf {SL}_{2})^{n}$ by its maximal central subgroup, as well as of the corresponding split reductive group. We also provide an example illustrating that a modification of our method can be applied to find the semi-decomposable invariants of a split semisimple group of type A.


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Additional Information

Sanghoon Baek
Affiliation: Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Republic of Korea
Email: sanghoonbaek@kaist.ac.kr

DOI: https://doi.org/10.1090/tran/6772
Received by editor(s): March 4, 2015
Published electronically: May 3, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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