A Splitting Criterion for Galois Representations Associated to Exceptional Modular Forms (mod p)

Details A Splitting Criterion for Galois Representations Associated to Exceptional Modular Forms (mod p) A Splitting Criterion for Galois Representations Associated to Exceptional Modular Forms (mod p)

2002-03-14

arxiv.org/abs/math/0203134v2

Mathematics

Number Theory

14 pages, no figures

Scientific paper

This paper continues the study of certain two-dimensional Galois representations attached to modular forms (mod p) via a construction due to Deligne. In particular, we prove a criterion for determining when the representation is split when restricted to a decomposition group at p.While this problem was already well understood for "nonexceptional" modular forms, here we specifically address the "exceptional" case. Although the problem is not solved in all generality, it is reasonable to hope that this proof will in fact provide the framework of a proof in the more general case.

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