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Number Theory Seminar

Thursday, January 16, 2020
4:00pm to 5:00pm
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Linde Hall 310
Local p-indecomposability of modular p-adic Galois representations
Haruzo Hida, Department of Mathematics, UCLA,

A conjecture by R. Greenberg asserts that a modular 2-dimensional p-adic Galois representation of a cusp form of weight larger than or equal to 2 is indecomposable over the p-inertia group unless it is induced from an imaginary quadratic field. I start with a survey of the known results and try to reach a brief description of a new case of indecomposability. Fix a prime p ≥ 3 and an absolutely irreducible odd representation ρ : Gal(Q/Q) → GL2(F) (F/Fp finite) of prime-to-p conductor 0 < N ∈ Z.

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