Companion points and locally analytic socle for GL₂(L)

2016/02/29 by Yiwen Ding, Ding, Yiwen
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1602.08859

openalex publication_date 2016/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p>2 be a prime number, and L be a finite extension of ℚ_p, we prove Breuil's locally analytic socle conjecture for GL₂(L), showing the existence of all the companion points on the definite (patched) eigenvariety. This work relies on infinitesimal "R=T" results for the patched eigenvariety and the comparison of (partially) de Rham families and (partially) Hodge-Tate families. This method allows in particular to find companion points of non-classical points.

Related

• Some results on locally analytic socle for GL_n(ℚ_p)
• Companion points and locally analytic socle conjecture for Steinberg case
• The Local Companion Points Conjecture
• On the locally analytic Ext¹-conjecture in the GL₂(L) case
• Patching and the p-adic local Langlands correspondence