Explicit Drinfeld moduli schemes and Abhyankar's Generalized Iteration Conjecture.

Text Let k be a field containing F q . Let ψ be a rank r Drinfeld F q [ t ] -module determined by ψ t ( X ) = t X + a 1 X q + ⋯ + a r − 1 X q r − 1 + X q r , where t , a 1 , … , a r − 1 are algebraically independent over k . Let n ∈ F q [ t ] be a monic polynomial. We show that the Galois group of ψ n ( X ) over k ( t , a 1 , … , a r − 1 ) is isomorphic to GL r ( F q [ t ] / n F 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 . [ABSTRACT FROM AUTHOR]