Derivatives of Frobenius and Derivatives of Hodge—Tate Weights

  • Bing Yong XieEmail author


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.


Fontaine-Mazur \(\mathcal{L}\)-invariant Galois representation 

MR(2010) Subject Classification



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Part of this work was done while the author was a visitor at Shanghai Center for Mathematical Sciences. The author is grateful to this institution for its hospitality. The author thanks Liang Xiao for his helpful discussion.


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© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.Department of MathematicsEast China Normal UniversityShanghaiP. R. China

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