论文标题
Abhyankar的仿射算术猜想是对称和交替组的
Abhyankar's Affine Arithmetic Conjecture for the Symmetric and Alternating Groups
论文作者
论文摘要
我们证明，对于任何Prime $ p> 2 $，$ q = p = p^ν$，$ p $，$ n \ ge p $和$ g = s_n $或$ g = a_n $（对称或交替的群体）的功率仅存在$ k/\ k/\ mathbb f_q（t）$ ramifient $ k/\ ram for $ \ flm $ \ \ \ vall \ gall \ gall \ wall \ wallm van（ f_q（t））= g $。这证实了abhyankar的猜想是对称和交替组的奇数特征的对称和交替组的情况。
We prove that for any prime $p>2$, $q=p^ν$ a power of $p$, $n\ge p$ and $G=S_n$ or $G=A_n$ (symmetric or alternating group) there exists a Galois extension $K/\mathbb F_q(T)$ ramified only over $\infty$ with $\mathrm{Gal}(K/\mathbb F_q(T))=G$. This confirms a conjecture of Abhyankar for the case of symmetric and alternating groups over finite fields of odd characteristic.
