On Galois Representations of Weight One

A two-dimensional Galois representation into the Hecke algebra of Katz modular forms of weight one over a finite field of characteristic $p$ is constructed and is shown to be unramified at $p$ in most cases.

2010 Mathematics Subject Classification: Primary 11F80M Secondary 11F33, 11F25

Keywords and Phrases: Galois representations, modular forms of weight one, Hecke algebras

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