休眠歌剧轨迹的程度
The degree of the dormant operatic locus
摘要：
设$X$是特征为$p>0$的代数闭域上亏格为$g\geq 2$的光滑射影曲线.本文给出了休眠${\rm PGL}(r)$ -opers在$X$上的度的解析公式，其中$r\geq 2$（假定$p$大于一个依赖于$g,r$的显式常数）.对于$r=2$来说，休眠的${\rm PGL}(2)$ -oper是在Shinichi Mochuzki的意义上$X$上的休眠的固有束（并且他的工作从不同的角度提供了仅用于$g=2,r=2,p\geq 5$的公式）。最近Yasuhiro Wakabayashi证明了我的数学公式对$X$通用型、$r\geq 2$和$p$大型型都成立。
英文摘要：
Let $X$ be a smooth, projective curve of genus $g\geq 2$ over an algebraically closed field of characteristic $p>0$. I provide a conjectural formula for the degree of the scheme of dormant ${\rm PGL}(r)$-opers on $X$ where $r\geq 2$ (I assume that $p$ is greater than an explicit constant depending on $g,r$). For $r=2$ a dormant ${\rm PGL}(2)$-oper is a dormant indigenous bundle on $X$ in the sense of Shinichi Mochuzki (and his work provides a formula only for $g=2,r=2,p\geq 5$, from a different point of view). Recently Yasuhiro Wakabayashi has shown that my conjectural formula holds for $X$ generic, $r\geq 2$ and $p$ large.
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