Companion points and locally analytic socle for GL2(L)

• Published in: Israel journal of mathematics Vol. 231; no. 1; pp. 47 - 122
• Main Author: Ding, Yiwen
• Format: Journal Article
• Language: English
• 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

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...