A generalization of Colmez-Greenberg-Stevens formula

TL;DR

This paper generalizes the Colmez-Greenberg-Stevens formula by studying derivatives of Frobenius and Hodge-Tate weights in Galois representation families, introducing a new generalized Fontaine-Mazur L-invariant.

Contribution

It introduces a generalized Fontaine-Mazur L-invariant and extends the Colmez-Greenberg-Stevens formula to broader classes of Galois representations.

Findings

Generalized Fontaine-Mazur L-invariant for Galois families

Extended Colmez-Greenberg-Stevens formula

New relations between derivatives of Frobenius and Hodge-Tate weights

Abstract

In this paper we study the derivatives of Frobenius and the derivatives of Hodge-Tate weights for families of Galois representations with triangulations. We give a generalization of the Fontaine-Mazur L-invariant and use it to build a formula which is a generalization of the Colmez-Greenberg-Stevens formula.