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 generalize the Fontaine—Mazur $$\mathcal{L}$$ -invariant and use it to build a formula which is a generalization of the Colmez—Greenberg—Stevens formula. For the purpose of proving this formula we show two auxiliary results called projection vanishing property and “projection vanishing implying $$\mathcal{L}$$ -invariants” property.
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