Wildly Ramified Galois Representations and a Generalization of a Conjecture of Serre

Abstract

Serre's conjecture relates two-dimensional odd irreducible characteristic p representations to modular forms. We discuss a generalization of this conjecture (due to Ash and Sinnott) to higherdimensional Galois representations. In particular, we give a refinement of the conjecture in the case of wildly ramified Galois representations and we provide computational evidence for this refinement.

Keywords:

• Primary 11F80
• Secondary 11F75
• Galois representations
• cohomology
• reciprocity laws
• Serre's conjecture