Triangulation of refined families

  • Ruochuan Liu

    Peking University, Beijing, China

Abstract

We prove the global triangulation conjecture for families of refined -adic representations under a mild condition. That is, for a refined family, the associated family of -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].

Cite this article

Ruochuan Liu, Triangulation of refined families. Comment. Math. Helv. 90 (2015), no. 4, pp. 831–904

DOI 10.4171/CMH/372