Geodesic
The structure of formal modules as Galois modules in cyclic unramified $p$-extensions
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 37, Tome 500 (2021), pp. 37-50

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The structure of the formal module $F(\mathfrak{M})$ for a chain of finite extensions $M/L/K$, where $M/L$ is an unramified $p$-extension, is studied. The triviality of the first Galois cohomology of a formal module for an unramified extension for any degree of a prime ideal is shown. The presentation of the investigated formal module is constructed in terms of generators and relations. As an application of the main result, the structure of a formal module for generalized Lubin–Tate formal groups is obtained. 
@article{ZNSL_2021_500_a3,
     author = {S. V. Vostokov and V. M. Polyakov},
     title = {The structure of formal modules as {Galois} modules in cyclic unramified $p$-extensions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {37--50},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_500_a3/}
}
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S. V. Vostokov; V. M. Polyakov. The structure of formal modules as Galois modules in cyclic unramified $p$-extensions. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 37, Tome 500 (2021), pp. 37-50. http://geodesic.mathdoc.fr/item/ZNSL_2021_500_a3/