Commentarii Mathematici Helvetici

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Volume 90, Issue 4, 2015, pp. 831–904
DOI: 10.4171/CMH/372

Published online: 2015-12-03

Triangulation of refined families

Ruochuan Liu[1]

(1) Peking University, Beijing, China

We prove the global triangulation conjecture for families of refined $p$-adic representations under a mild condition. That is, for a refined family, the associated family of $(\varphi, \Gamma)$-modules admits a global triangulation on a Zariski open and dense subspace of the base that contains all regular non-critical points. We also determine a large class of points which belongs to the locus of global triangulation. Furthermore, we prove that all the specializations of a refined family are trianguline. In the case of the Coleman–Mazur eigencurve, our results provide the key ingredient for showing its properness in a subsequent work [15].

Keywords: $p$-adic Galois representations, overconvergent automorphic forms, global triangulation

Liu Ruochuan: Triangulation of refined families. Comment. Math. Helv. 90 (2015), 831-904. doi: 10.4171/CMH/372