Explicit Drinfeld moduli schemes and Abhyankar's Generalized Iteration Conjecture

JOURNAL OF NUMBER THEORY

卷:160

Article

Breuer, Florian¹ 

[1] Univ Stellenbosch, ZA-7600 Stellenbosch, South Africa

关键词: Drinfeld modules;    Drinfeld moduli schemes;    Galois groups;   

DOI  :  10.1016/j.jnt.2015.08.021

来源: Elsevier

【 摘 要 】

Text. Let k be a field containing F-q. Let psi be a rank r Drinfeld F-q[t]-module determined by psi(t) (X) = tX + a(1)X(q) + . . . + a(r-1) Xq'-1 + X-qr , where t, a1, . . . , a(r-1) are algebraically independent over k. Let n is an element of F-q [t] be a monic polynomial. We show that the Galois group of psi(n)(X) over k(t, a(1), . . . , a(r-1)) is isomorphic to GL(r)-(F-q[t]/nF(q)[t]), settling a conjecture of Abhyankar. Along the way we obtain an explicit construction of Drinfeld moduli schemes of level tn. Video. For a video summary of this paper, please visit https://youtu.be/TInrNq02-UA. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free