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In this paper we study the derivatives of Frobenius and the derivatives ofHodge weights for families of Galois representations with triangulations. Wegeneralize the Fontaine-Mazur L-invariant and use it to build a formula whichis a generalization of the Greenberg-Stevens-Colmez formula. For the purpose ofproving this formula we show two auxiliary results called projection vanishingproperty and "projection vanishing implying L-invariants" property.

Derivatives of Frobenius and Derivatives of Hodge weights