The equivariant Tamagawa number conjecture for $(h^0(\operatorname{Spec}(L)),\mathbb{Z}[G])$

Let $L/K$ be a finite Galois extension of number fields with Galois group $G$, and let $S$ be a finite set of places of $K$ containing all archimedean places and all places ramified in $L$. Let $T\Omega(L/K,0)$ be Burns's canonical element in the relative algebraic $K$-group $K_0(\mathbb{Z}[G],\mathbb{R})$, defined using the refined Euler characteristic and the leading term of the equivariant $S$-truncated $L$-series at $s=0$. Equivariant Tamagawa number conjecture. The element $T\Omega(L/K,0)$ vanishes:

$$T\Omega(L/K,0)=0\quad\text{in }K_0(\mathbb{Z}[G],\mathbb{R}).$$

This is the ETNC for the stated pair, and the source uses it as the conjectural statement underlying its results on the minus $p$-part under additional ramification hypotheses.