Galois Representations Associated to p-adic Families of Modular Forms of Finite Slope

2015/04/18 by Mihara, Tomoki
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1504.04728

Abstract

We define a pro-p Abelian sheaf on a modular curve of a fixed level N ≥ 5 divisible by a prime number p ≠ 2. Every p-adic representation of Gal(ℚ/ℚ) associated to an eigenform is obtained as a quotient of its étale cohomology. For any compact ℤ_p[[1 + N ℤ_p]]-algebra Λ₁ satisfying certain suitable conditions, we construct a representation of Gal(ℚ/ℚ) over Λ₁ associated to a Λ₁-adic cuspidal eigenform of finite slope as a scalar extension of a quotient of the étale cohomology.

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