Triangulation of refined families

Abstract

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 (phi, 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.

Final version

References in corpus (1)

• Sur la densité des représentations cristallines du groupe de Galois absolu de Q_p

Cited by in corpus (8)

• p-adic Cohomology and classicality of overconvergent Hilbert modular forms
• Cohomology of arithmetic families of (phi,Gamma)-modules
• Families of trianguline representations and finite slope spaces
• The Eigencurve is Proper
• $\mathcal{L}$-invariants and logarithm derivatives of eigenvalues of Frobenius
• $\mathcal{L}$-invariants, partially de Rham families and local-global compatibility
• On symmetric power L-invariants of Iwahori level Hilbert modular forms
• Some results on locally analytic socle for ${\mathrm{GL}}_n({\mathbb{Q}}_p)$