On a purely inseparable analogue of the Abhyankar Conjecture for affine curves

Abstract

Let $U$ be an affine smooth curve defined over an algebraically closed field of positive characteristic. The Abhyankar Conjecture (proved by Raynaud and Harbater in 1994) describes the set of finite quotients of Grothendieck's étale fundamental group of $U$. In this paper, we consider a purely inseparable analogue of this problem, formulated in terms of Nori's profinite fundamental group scheme, and give a partial answer to it.

2nd version. Added Remark 3.7(4). Filled a gap in Lemma 4.2. Corrected some typos

References in corpus (1)

• On the algebraic fundamental group of smooth varieties in characteristic $p>0$

Cited by in corpus (3)

• An embedding problem for finite local torsors over twisted curves
• The arithmetic local Nori fundamental group
• A generalized Abhyankar's conjecture for simple Lie algebras in characteristic $p>5$