Algebraic K-theory of the varieties 𝑆𝐿_{2𝑛}/𝑆𝑝_{2𝑛}, 𝐸₆/𝐹₄ and their twisted forms

Yakerson, Maria

doi:10.1090/spmj/1457

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

St. Petersburg Math. J. 28 (2017), 421-431

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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