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On a purely inseparable analogue of the Abhyankar conjecture for affine curves
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 8 / August 2018
- Published online by Cambridge University Press:
- 19 July 2018, pp. 1633-1658
- Print publication:
- August 2018
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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 
$\unicode[STIX]{x1D70B}_{1}^{\acute{\text{e}}\text{t}}(U)$. In this paper, we consider a purely inseparable analogue of this problem, formulated in terms of Nori’s profinite fundamental group scheme 
$\unicode[STIX]{x1D70B}^{N}(U)$, and give a partial answer to it.
