论文标题
刚性本地系统和有限的通用线性组
Rigid local systems and finite general linear groups
论文作者
论文摘要
We use hypergeometric sheaves on $G_m/F_q$, which are particular sorts of rigid local systems, to construct explicit local systems whose arithmetic and geometric monodromy groups are the finite general linear groups $GL_n(q)$ for any $n \ge 2$ and and any prime power $q$, so long as $q > 3$ when $n=2$.本文继续一项计划，即发现简单的（在简单地记住的意义上）指数级的家族，其单型群是某些有限的谎言类型组，请参见。 [gr]，[kt1]，[kt2]，[kt3]用于（某些）有限的符号和统一组，或某些零星群体，请参见。 [KRL]，[KRLT1]，[KRLT2]，[KRLT3]。本文的新颖性是以这种超几何学方式获得$ gl_n（q）$。然后，回调构造会在$ a^1/f_q $上产生本地系统，其几何单型组为$ sl_n（q）$。这些结果是为了恢复Abhyankar的结构。
We use hypergeometric sheaves on $G_m/F_q$, which are particular sorts of rigid local systems, to construct explicit local systems whose arithmetic and geometric monodromy groups are the finite general linear groups $GL_n(q)$ for any $n \ge 2$ and and any prime power $q$, so long as $q > 3$ when $n=2$. This paper continues a program of finding simple (in the sense of simple to remember) families of exponential sums whose monodromy groups are certain finite groups of Lie type, cf. [Gr], [KT1], [KT2], [KT3] for (certain) finite symplectic and unitary groups, or certain sporadic groups, cf. [KRL], [KRLT1], [KRLT2], [KRLT3]. The novelty of this paper is obtaining $GL_n(q)$ in this hypergeometric way. A pullback construction then yields local systems on $A^1/F_q$ whose geometric monodromy groups are $SL_n(q)$. These turn out to recover a construction of Abhyankar.
