English

The $\mathcal{L}$-invariant, the dual $\mathcal{L}$-invariant, and families

Number Theory 2015-12-04 v1

Abstract

Given a rank two trianguline family of (φ,Γ)(\varphi,\Gamma)-modules having a noncrystalline semistable member, we compute the Fontaine--Mazur L\mathcal{L}-invariant of that member in terms of the logarithmic derivative, with respect to the Sen weight, of the value at p of the trianguline parameter. This generalizes prior work, in the case of Galois representations, due to Greenberg--Stevens and Colmez.

Keywords

Cite

@article{arxiv.1512.00930,
  title  = {The $\mathcal{L}$-invariant, the dual $\mathcal{L}$-invariant, and families},
  author = {Jonathan Pottharst},
  journal= {arXiv preprint arXiv:1512.00930},
  year   = {2015}
}

Comments

accepted to Annales math\'ematiques du Qu\'ebec (special volume in honor of Glenn Stevens's 60th birthday)