Fukaya–Kato equivariant integrality conjecture

Let $F/\mathbb Q$ be a $p$-adic Lie extension with Galois group $G$, let $\Lambda=\Lambda(G)$ be its Iwasawa algebra, let $T_p$ be a Galois-stable lattice, and put $\mathbb T=\Lambda\otimes_{\mathbb Z_p}T_p$. For a finite coefficient extension with representation $\rho$ as in the source, write $T_\lambda(M(\rho^*))$ for the corresponding lattice. Fukaya–Kato equivariant integrality conjecture. There exists a unique isomorphism

$$\zeta_\Lambda(M):=\zeta_\Lambda(\mathbb T):\mathbf{1}_\Lambda\to\mathcal D_\Lambda(\mathrm{R}\Gamma_c(U,\mathbb T))^{-1}$$

whose base change under $\mathcal O_\lambda^n\otimes_\Lambda-$ is $\zeta_{\mathcal O_\lambda}(T_\lambda(M(\rho^*)))$ for all such $K,\lambda,\rho$. This is the equivariant integral refinement of the Tamagawa-number conjecture in noncommutative Iwasawa theory; the source attributes the formulation to Fukaya and Kato.