An equivariant Tamagawa number formula for Drinfeld modules and applications

We fix data $(K/F, E)$ consisting of a Galois extension $K/F$ characteristic $p$ global fields with arbitrary abelian group $G$ and Drinfeld module $E$ defined over certain Dedekind subring $F$. For this data, we define $G$-equivariant $L$-function $\Theta_{K/F}^E$ prove an equivariant Tamagawa number formula for Euler-completed versions its special value $\Theta_{K/F}^E(0)$. This generalizes Taelman's class the $\zeta_F^E(0)$ Goss zeta function $\zeta_F^E$ associated to pair $(F, E)$. result is obtained from our by setting $K=F$. As consequence, perfect analogue classical (number field) refined Brumer--Stark conjecture, relating $G$-Fitting ideal $H(E/K)$ $\Theta_{K/F}^E(0)$ in question.