$\mathcal{L}$-invariants and logarithm derivatives of eigenvalues of Frobenius

Abstract

Let $K$ be a $p$-adic local field. In this work we study a special kind of $p$-adic Galois representations of it. These representations are similar to the Galois representations occurred in the exceptional zero conjecture for modular forms. In particular, we verify that a formula of Colmez can be generalized to our case. We also include a degenerated version of Colmez's formula.

References in corpus (1)

• Triangulation of refined families

Cited by in corpus (2)

• $\mathcal{L}$-invariants, partially de Rham families and local-global compatibility
• Higher $\mathcal{L}$-invariants for ${\mathrm{GL}}_3({\mathbb{Q}}_p)$ and local-global compatibility