Diamond diagrams and multivariable (φ,O_K^×)-modules

2025/04/12 by Wang, Yitong
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.09270

Abstract

Let p be a prime number and K a finite unramified extension of ℚ_p. Let π be an admissible smooth mod p representation of GL₂(K) occurring in some Hecke eigenspaces of the mod p cohomology and r be its underlying global two-dimensional Galois representation. When r satisfies some Taylor-Wiles hypotheses and is sufficiently generic at p, we compute explicitly certain constants appearing in the diagram associated to π, generalizing the results of Dotto-Le. As a result, we prove that the associated étale (φ,O_K^×)-module D_A(π) defined by Breuil-Herzig-Hu-Morra-Schraen is explicitly determined by the restriction of r to the decomposition group at p, generalizing the results of Breuil-Herzig-Hu-Morra-Schraen and the author.

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