Geodesic
The Hasse conjecture for cyclic extensions
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 197-204

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In the present paper, embedding conditions for a quadratic extension of an algebraic number field into a cyclic 2-extension are presented. An example of an unsolvable embedding problem for which the compatibility condition is fulfilled is constructed. 
@article{ZNSL_2005_321_a8,
     author = {V. V. Ishkhanov and B. B. Lur'e},
     title = {The {Hasse} conjecture for cyclic extensions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {197--204},
     publisher = {mathdoc},
     volume = {321},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a8/}
}
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V. V. Ishkhanov; B. B. Lur'e. The Hasse conjecture for cyclic extensions. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 197-204. http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a8/