论文标题
较高级别的差分模块和休眠操作
Differential modules and dormant opers of higher level
论文作者
论文摘要
在本文的上半年中，我们研究了积极特征中差分模块的更高层次概括。这些对象可以被视为曲线上的矢量束的环理论对应物，该曲线配备了P. Berthelot（和C. Montagnon）引入的有限级别（对数）差分运算符的环的动作。在轻度条件下，差异模块的循环载体的存在被推广到更高水平。在下半年，我们在尖的平滑曲线上介绍了级别$ n> 0 $的（休眠）Opers，其结构组为$ \ mathrm {gl} _n $或$ \ mathrm {pgl} _n $。应用高级微分模块上的某些结果用于证明二元$ \ Mathrm {pgl} _n $ - 级别$ n $的二重性定理与级别的$ n $级别的$ n $ opers j {pgl} _ {p^n-n-n} $ - 最后，在基础曲线为$ 3 $点的投影线的情况下，我们在休眠$ \ mathrm {pgl} _2 $ n $ level $ n $和某些tamely tamely tamifiew的封面之间建立了两种义工的对应关系。
In the first half of the present paper, we study higher-level generalizations of differential modules in positive characteristic. These objects may be regarded as ring-theoretic counterparts of vector bundles on a curve equipped with an action of the ring of (logarithmic) differential operators of finite level introduced by P. Berthelot (and C. Montagnon). The existence assertion for a cyclic vector of a differential module is generalized to higher level under mild conditions. In the second half, we introduce (dormant) opers of level $N > 0$ on a pointed smooth curve whose structure group is either $\mathrm{GL}_n$ or $\mathrm{PGL}_n$. Some of the results on higher-level differential modules are applied to prove a duality theorem between dormant $\mathrm{PGL}_n$-opers of level $N$ and dormant $\mathrm{PGL}_{p^N-n}$-opers of level $N$. Finally, in the case where the underlying curve is a $3$-pointed projective line, we establish a bijective correspondence between dormant $\mathrm{PGL}_2$-opers of level $N$ and certain tamely ramified coverings.
