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In a previous paper we constructed a new class of Iwasawa modules as$\ell$--adic realizations of what we called abstract $\ell$--adic $1$--motivesin the number field setting. We proved in loc. cit. that the new Iwasawamodules satisfy an equivariant main conjecture. In this paper we link the newmodules to the $\ell$--adified Tate canonical class, defined by Tate in 1960and give an explicit construction of (the minus part of) $\ell$--adic Tatesequences for any Galois CM extension $K/k$ of an arbitrary totally real numberfield $k$. These explicit constructions are significant and useful in their ownright but also due to their applications (via our previous results on theEquivariant Main Conjecture in Iwasawa theory) to a proof of the minus part ofthe far reaching Equivariant Tamagawa Number Conjecture for the Artin motiveassociated to the Galois extension $K/k$.

Abstract $\ell$-adic $1$-motives and Tate's class