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Companion points and locally analytic socle for GL2(L)

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Abstract

Let L be a finite extension of ℚp. We prove under mild hypotheses 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.

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Authors and Affiliations

  1. Beijing International Centre for Mathematical Research, Peking University, Beijing, 100871, China

    Yiwen Ding

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  1. Yiwen Ding
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Correspondence to Yiwen Ding.

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This work was supported by EPSRC grant EP/L025485/1.

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Ding, Y. Companion points and locally analytic socle for GL2(L). Isr. J. Math. 231, 47–122 (2019). https://doi.org/10.1007/s11856-019-1845-y

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  • DOI: https://doi.org/10.1007/s11856-019-1845-y

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