A generalized Abhyankar's conjecture for simple Lie algebras in characteristic $p>5$
Algebraic Geometry
2021-10-07 v2 Number Theory
Representation Theory
Abstract
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 . 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.
Keywords
Cite
@article{arxiv.2003.03240,
title = {A generalized Abhyankar's conjecture for simple Lie algebras in characteristic $p>5$},
author = {Shusuke Otabe and Fabio Tonini and Lei Zhang},
journal= {arXiv preprint arXiv:2003.03240},
year = {2021}
}