有理函数域的约化理论
Reduction theory for a rational function field
摘要：
设$G$是有限域$\Fq$上的可裂约化群.令$F=\Fq(t)$和$\A$表示$F$的子集。我们证明了$G(F)\bsl G(\A)/ K$中的每一个双陪集在$G$的最大分裂环面中都有一个代表。这里$K$是$G$的积分adélic点的集合。当$G$的范围在一般线性群上时，这等价于断言射影线上的任何代数向量丛同构于线丛的直和。
英文摘要：
Let $G$ be a split reductive group over a finite field $\Fq$. Let $F=\Fq(t)$ and let $\A$ denote the adèles of $F$. We show that every double coset in $G(F)\bsl G(\A)/ K$ has a representative in a maximal split torus of $G$. Here $K$ is the set of integral adèlic points of $G$. When $G$ ranges over general linear groups this is equivalent to the assertion that any algebraic vector bundle over the projective line is isomorphic to a direct sum of line bundles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
