论文标题
广义的Abhyankar对特征中简单谎言代数的猜想$ p> 5 $
A generalized Abhyankar's conjecture for simple Lie algebras in characteristic $p>5$
论文作者
论文摘要
在本文中，我们研究了Abhyankar对仿射线的纯粹不可分割的对应物，并证明了其对所有有限的本地非亚洲简单组方案的有效性，特征性$ p> 5 $。关键点是如何应对有限的本地组方案，这些方案无法实现为平滑代数群体的Frobenius内核。这样的组方案似乎是与cartan类型相关的代数相关的方案。我们通过利用自然等级或过滤来解决此类代数的问题。
In the present paper, we study a purely inseparable counterpart of Abhyankar's conjecture for the affine line in positive characteristic, and prove its validity for all the finite local non-abelian simple group schemes in characteristic $p>5$. The crucial point is how to deal with finite local group schemes which cannot be realized as the Frobenius kernel of a smooth algebraic group. Such group schemes appear as the ones associated with Cartan type Lie algebras. We settle the problem for such Lie algebras by making use of natural gradations or filtrations on them.
