Arithmetic actions on cyclotomic function fields

2018/07/06 by Kontogeorgis, Aristides, Ward, Jacob Kenneth
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1807.02220

Abstract

We derive the group structure for cyclotomic function fields obtained by applying the Carlitz action for extensions of an initial constant field. The tame and wild structures are isolated to describe the Galois action on differentials. We show that the associated invariant rings are not polynomial.

Related

• Galois Groups and Genera of a kind of Quasi-cyclotomic Function Fields
• The Spiegelungssatz for the Carlitz module
• Nontrivial Galois module structure of cyclotomic fields
• Explicit Galois representations of automorphisms on holomorphic differentials in characteristic p
• Cyclotomic function fields over finite fields with irreducible quadratic modulus