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Algebraic K-theory of the varieties $ \mathrm{SL}_{2n} / \mathrm{Sp}_{2n}$, $ \mathrm{E}_6 / \mathrm{F}_4$ and their twisted forms


Author: Maria Yakerson
Translated by: the author
Original publication: Algebra i Analiz, tom 28 (2016), nomer 3.
Journal: St. Petersburg Math. J. 28 (2017), 421-431
MSC (2010): Primary 19E08; Secondary 14M17
DOI: https://doi.org/10.1090/spmj/1457
Published electronically: March 29, 2017
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Abstract: Let $ \mathrm {SL}_{2n}$, $ \mathrm {Sp}_{2n}$, $ \mathrm {E}_6 = G^{sc}(\mathrm {E}_6)$, $ \mathrm {F}_4 = G(\mathrm {F}_4)$ be simply connected split algebraic groups over an arbitrary field $ F$. Algebraic K-theory of the affine homogeneous varieties $ \mathrm {SL}_{2n}/\mathrm {Sp}_{2n}$ and $ \mathrm {E}_6/\mathrm {F}_4$ is computed. Moreover, explicit elements that generate $ K_*(\mathrm {SL}_{2n}/\mathrm {Sp}_{2n})$ and $ K_*(\mathrm {E}_6/\mathrm {F}_4)$ as $ K_*(F)$-algebras are provided. Also, K-theory is computed for some twisted forms of these varieties.


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Additional Information

Maria Yakerson
Affiliation: Department of Mathematics, University of Duisburg-Essen Thea-Leymann-Str. 9 45127, Essen, Germany
Email: mura.yakerson@gmail.com

DOI: https://doi.org/10.1090/spmj/1457
Keywords: Algebraic K-theory, affine homogeneous varieties
Received by editor(s): October 24, 2015
Published electronically: March 29, 2017
Additional Notes: Supported by the grant Sonderforschungsbereich Transregio 45
Dedicated: To Sasha Ivanov
Article copyright: © Copyright 2017 American Mathematical Society