The K-Theory of Versal Flags and Cohomological Invariants of Degree 3

Let $G$ be a split semisimple linear algebraic group over a field and let
$X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis
techniques to Laurent polynomials over integers we give an explicit presentation
of the Grothendieck ring $K_{0}(X)$ in terms of generators and relations
in the case $G=G^{sc}/\mu_{2}$ is of Dynkin type ${A}$ or ${C}$ (here
$G^{sc}$ is the simply-connected cover of $G$); we compute various groups
of (indecomposable, semi-decomposable) cohomological invariants of degree
3, hence, generalizing and extending previous results in this direction.

2010 Mathematics Subject Classification: 14M17, 20G15, 14C35

Keywords and Phrases: linear algebraic group, twisted flag variety, ideal of invariants, versal torsor, cohomological invariant

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