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 $K₀(X)$ in terms of generators and relations in the case $G=G^sc/\mu₂$ 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

Full text: dvi.gz 71 k, dvi 232 k, ps.gz 431 k, pdf 377 k.

Home Page of DOCUMENTA MATHEMATICA