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We study a conjecture of Tsfasman and Vladuts which posits a general versionof the Brauer--Siegel theorem for any asymptotically exact family of numberfields. We suggest an approach which, not only allows to unify the proofs ofseveral previous results towards this conjecture as well as generalise these toa relative setting, but also yields new unconditional cases of the conjecture.We exhibit new sets of conditions which ensure that a family of number fieldsunconditionally satisfies the conjecture of Tsfasman and Vladuts. We thus provethat this conjecture holds for any asymptotically good family of number fieldscontained in the solvable closure of a given number field. We further give anumber of explicit examples of such families, such as that of an infiniteglobal field contained in a $p$-class field tower.

Sur le th\'eor\`eme de Brauer--Siegel g\'en\'eralis\'e