Refinement of Tate's Discriminant Bound and Non-Existence Theorems for Mod $p$ Galois Representations

Non-existence is proved of certain continuous irreducible mod $p$ representations of degree 2 of the absolute Galois group of the rational number field. This extends previously known results, the improvement based on a refinement of Tate's discriminant bound.

2000 Mathematics Subject Classification: 11F80, 11R29, 11R39

Keywords and Phrases: Mod $p$ Galois Representation, Discriminant

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