  In \cite{FGHP}, the first author and his collaborators proved an equivariant
Tamagawa number formula for the special value at $s=0$ of a Goss--type
$L$--function, equivariant with respect to a Galois group $G$, and associated
to a Drinfeld module defined on $\Bbb F_q[t]$ and over a finite, integral
extension of $\Bbb F_q[t]$. The formula in question was proved provided that
the values at $0$ of the Euler factors of the equivariant $L$--function in
question satisfy certain identities involving Fitting ideals of certain
$G$--cohomologically trivial, finite $\Bbb F_q[t][G]$--modules associated to
the Drinfeld module. In \cite{FGHP}, we prove these identities in the
particular case of the Carlitz module. In this paper, we develop general
techniques and prove the identities in question for arbitrary Drinfeld modules.
Further, we indicate how these techniques can be extended to the more general
case of higher dimensional abelian $t$--modules, which is relevant in the
context of the proof of the equivariant Tamagawa number formula for abelian
$t$--modules given by N. Green and the first author in \cite{Green-Popescu}.
This paper is based on a lecture given by the first author at ICMAT Madrid in
May 2023 and builds upon results obtained by the second author in his PhD
thesis \cite{Ramachandran-thesis}.
