On the Inertia Conjecture for Alternating group covers

Article Type

Research Article

Publication Title

Journal of Pure and Applied Algebra

Abstract

Let G1 and G2 be perfect groups such that there exist connected G1-Galois and G2-Galois étale covers of the affine line over an algebraically closed field of characteristic p>0 with the cyclic p-groups P1 and P2 as the inertia groups above ∞, respectively. Then we show that there is a connected G1×G2-Galois étale cover of the affine line with an inertia group I above ∞ where I is a cyclic subgroup of P1×P2 of index p. As a consequence, it is shown that the wild part of the Inertia Conjecture is true for any product of Alternating groups, each of degree p or coprime to p. For d a multiple of p, a new étale Ad-cover of the affine line is obtained using an explicit equation, and it is shown that this cover has the minimal possible upper jump.

DOI

10.1016/j.jpaa.2020.106363

Publication Date

9-1-2020

Comments

Open Access, Green

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