Companion points and locally analytic socle for GL2(L)

Let L be a finite extension of ℚ p . We prove under mild hypotheses Breuil’s locally analytic socle conjecture for GL 2 ( 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 an...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 231; no. 1; pp. 47 - 122
Main Author Ding, Yiwen
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.05.2019
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:Let L be a finite extension of ℚ p . We prove under mild hypotheses Breuil’s locally analytic socle conjecture for GL 2 ( 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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-019-1845-y