论文标题
在一个代数组的基本维度上，其连接的组件是圆环
On the essential dimension of an algebraic group whose connected component is a torus
论文作者
论文摘要
让$ p $为主要整数，$ k $是$ p $ cluct的特征$ \ neq p $，$ t $的字段，$ t $是$ k $定义的圆环，$ f $是有限的$ p $ - group，$ 1 \ $ 1 \ to t \ t \ t to t to t to f \ to f \ to f f \ to 1 $是algebraic组的精确序列。扩展了N. Karpenko和A. Merkurjev，R.Lötscher，M。Macdonald，A。Meyer的早期工作，第一作者以及第一作者表明，\ [\ min \ dim \ dim \ dim \ min \ dim \ dim（g） $ v $和$ w $范围分别超过$ p $ - 信仰和$ p $ - 分别为$ g $的$ k $ - 代表。他们猜想上限实际上是锋利的。这个猜想已经开放了一段时间。我们在这种情况下证明了这一点，其中$ f $是可对角线的。
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 $1\to T \to G \to F \to 1$ be an exact sequence of algebraic groups. Extending earlier work of N. Karpenko and A. Merkurjev, R. Lötscher, M. MacDonald, A. Meyer, and the first author showed that \[\min\dim(V) - \min\dim(G) \leqslant \text{ed}(G; p) \leqslant \min \dim(W) - \dim(G),\] 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.
