Explicit Galois representations of automorphisms on holomorphic\n differentials in characteristic p

2014/08/27 by Kenneth Ward, Ward, Kenneth, Kenneth D. Ward
Mathematics · #11G09 #11R58 #11R60 #13N05 #14H37 (primary) #14H55 (secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1408.6391

openalex publication_date 2014/08/27 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We determine the representation of the group of automorphisms for cyclotomic\nfunction fields in characteristic p > 0 induced by the natural action on the\nspace of holomorphic differentials via construction of an explicit basis of\ndifferentials. This includes those cases which present wild ramification and\nautomorphism groups with non-cyclic p-part, which have remained elusive. We\nalso obtain information on the gap sequences of ramified primes. Finally, we\nextend these results to rank one Drinfel'd modules.\n

Citations

• Representation of cyclic groups in positive characteristic and Weierstrass semigroups

Related

• Ramification filtration and differential forms
• Characteristic p Galois representations that are produced by Drinfeld
• Arithmetic actions on cyclotomic function fields
• Representations of field automorphism groups
• Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields