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• W3013103162 abstract "Let $p$ be a prime integer, $k$ be a $p$-closed field of characteristic $neq p$, $T$ be a torus defined over $k$, $F$ be a finite $p$-group, and $1to T to G to F to 1$ be an exact sequence of algebraic groups. Extending earlier work of N. Karpenko and A. Merkurjev, R. Lotscher, M. MacDonald, A. Meyer, and the first author showed that [mindim(V) - mindim(G) leqslant text{ed}(G; p) leqslant min dim(W) - dim(G),] where $V$ and $W$ range over the $p$-faithful and $p$-generically free $k$-representations of $G$, respectively. They conjectured that the upper bound is, in fact, sharp. This conjecture has remained open for some time. We prove it in the case, where $F$ is diagonalizable." @default.
• W3013103162 created "2020-04-03" @default.
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• W3013103162 date "2020-03-25" @default.
• W3013103162 modified "2023-09-27" @default.
• W3013103162 title "On the essential dimension of an algebraic group whose connected component is a torus" @default.
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