Drinfeld Iterations and Wagner's Theorem

Abstract

In a previous paper, the author, in collaboration with Abhyankar, has proved that under certain assumptions the Galois groups of Carlitz–Drinfeld iterates of linear polynomials are general linear groups. The proof used Cameron–Kantor's characterization of linear groups. In this paper, we recover the result in very generic case by using a more elementary Wagner's characterization of linear groups. This is done using some commutative algebra.

Key Words:

• Iteration
• Perspectivity
• Linear group
• Very generic case

2000 AMS Subject Classification:

• 12
• 13
• 14
• 20G
• 51A

Acknowledgments

Notes

^#Communicated by R. Parimala.