Triangulation of refined families
By Ruochuan Liu. 2012
82 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/36a49fe010bc0f500520d148119e0a87a7fc7dda
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Analytic families of finite-slope Selmer groups (2013, methodology): “2012], a perfectness and duality result for the Galois cohomology of families of (φ, 0K )-modules is applied to give a general construction of triangulations of eigenvarieties as well as a classification of rank-one families of (φ, 0K )-modules; for other recent progress on triangulations, see [Chen”
- Iwasawa Main Conjecture for Supersingular Elliptic Curves (2014, background): “However it is not clear whether there are such families of triangulations at all points we need to study (see [47]).”
- Rankin–Eisenstein classes in Coleman families (2015, methodology): “In order to define the Perrin-Riou logarithm in this context, one needs to work with triangulations of (ϕ,Γ)-modules over the Robba ring; we use here results of Ruochuan Liu [Liu14], showing that the (ϕ,Γ)-modules of the Galois representationsMV1(F) ∗ and MV2(G) ∗ admit canonical triangulations.”