We provide corroborative evidence for the equivariant Tamagawa number conjecture which was formulated in the first part of this article.

We establish the equivalence of two definitions of invariants measuring the Galois module structure of K-groups of rings of integers in number fields (due to Chinburg et al. on the one hand and the authors on the other). We also make some remarks concerning the possibility of yet another such definition via Lichtenbaum complexes.

We establish various properties of the definition of cohomology of topological groups given by Grothendieck, Artin and Verdier in SGA4, including a Hochschild-Serre spectral sequence and a continuity theorem for compact groups. We use these properties to compute the cohomology of the Weil group of a totally imaginary field, and of the Weiletale topology of a number ring recently introduced by Lichtenbaum (both with integer coefficients).

Let f be a newform of weight k 2, level N with coefficients in a number field K, and A the adjoint motive of the motive M associated to f. We carefully discuss the construction of the realisations of M and A, as well as natural integral structures in these realisations. We then use the method of Taylor and Wiles to verify the λ-part of the Tamagawa number conjecture of Bloch and Kato for L(A, 0) and L(A, 1). Here λ is any prime of K not dividing Nk!, and so that the mod λ representation associated to f is absolutely irreducible when restricted to the Galois group over Q((−1) (−1)/2) where λ |. The method also establishes modularity of all lifts of the mod λ representation which are crystalline of Hodge-Tate type (0, k − 1).  2004 Elsevier SAS RÉSUMÉ.-Soient f une forme nouvelle de poids k, de conducteur N , à coefficients dans un corps de nombres K, et A le motif adjoint du motif M associé à f. Nous présentons en détail les réalisations des motifs M et A avec leurs réseaux entiers naturels. En utilisant les méthodes de Taylor-Wiles nous prouvons la partie λ-primaire de la conjecture de Bloch-Kato pour L(A, 0) et L(A, 1). Ici λ est une place de K ne divisant pas Nk! et telle que la représentation modulo λ associée à f , restreinte au groupe de Galois du corps Q((−1) (−1)/2) avec λ | , est irréductible. Notre méthode démontre aussi la modularité de toutes les représentations λ-adiques cristallines de type de Hodge-Tate (0, k − 1) congrues à la représentation associée à f modulo λ.

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