9 problems

Breuning's local equivariant epsilon constant conjecture.

Let $X$ be the regular arithmetic scheme considered above, of relative dimension $d$, and let $\Omega\in\widehat {\rm K}_0(X)$ be the arithmetic $K$-theory class represented by the…

Let $F/E$ be a weakly ramified Galois extension of $\ell$-adic fields with group $\Gamma$. Let $\mathfrak{a}_{F/E}$, $\mathcal{E}_{F/E}$, $J_{2,F/E}$, $\mathfrak{c}_{F/E}$ and…

The equivariant local Iwasawa main conjecture. There exists $\zeta^{(j)}_{L_\infty/K}\in K_1(\mathcal{Q}^c(\mathcal{G}))$ such that

Let $K$ be a finite extension of ${\mathbb Q}_p$, let $N/K$ be a finite Galois extension with Galois group $G$, and retain the notation $\tilde R_{N/K}$ and…

Let $K$ be a finite extension of ${\mathbb Q}_p$, let $N/K$ be a finite Galois extension with Galois group $G$, and let $T$ be a ${\mathbb Z}_p[G_K]$-lattice such that…

Let $F/E$ be a Galois extension with Galois group $Gamma$, and let $T\Omega^\mathrm{loc}(F/E,1)$ be the locally defined element of $K_0(\mathbb Z[\Gamma],\mathbb R)$. Global equiva…

Local epsilon constant conjecture. For every Galois extension $L_w/K_v$ of local fields over $\mathbb{Q}_p$,

Let $L/K$ be a finite Galois extension of number fields with Galois group $G$. Let $T\Omega^{\rm loc}(L/K,1)$ be the element of $K_0(\mathbb{Z}[G],\mathbb{Q})$ constructed from the…