8 problems

Let $k$ be an algebraically closed field of characteristic zero, and for $n\geq 1$ let … be the regulator map defined above. Regulator isomorphism conjecture. The regulator maps…

Let $F\colon \mathcal{M}\to\mathcal{N}$ be the functor appearing in the relative algebraic $K$-theory construction, and let $pB[F]$, $pC[F]$, $iB\mathcal{N}$, $iC\mathcal{N}$,…

Let $L/K$ be a weakly ramified Galois extension of number fields of odd degree. Write $\mathfrak{a}_{L/K}$ for the canonical pre-image associated with the stable-isomorphism class…

Let $R$ be a regular semi-local ring essentially of finite type over a perfect field, and let $n,p\geq 1$ with $n\neq p$. For each modulus $m\geq 1$, let ${\rm TCH}^p(R,n;m)$ denot…

Let $L/K$ be the Galois extension and $G=\operatorname{Gal}(L/K)$, with $G^+=G/\langle\tau\rangle$, and let $e_r$ denote the relevant idempotent. Let $L_{p,S}(r)$ be the central el…

Krishna–Levine spectral-sequence conjecture. There should exist a spectral sequence whose terms consist of these motivic cohomology groups and whose abutment is the relative $K$-th…

Let $A$ be the semisimple coefficient algebra acting on the motive $M$, let $i$ be an integer, and let $n>\frac{i}{2}+1$ be an integer. Write $L({}_A H^i(M),n)$ for the equivariant…

Let $A=\mathbb{Z}[x,y]/(xy)$ and let $I=(x,y)$. The low-dimensional relative K-theory conjecture. … and … These computations reduce to calculations of equivariant topological cycli…