4 problems

Let $R$ be a discrete valuation ring (DVR) with fraction field $K$, and let $A$ and $B$ be $n\times n$ matrices over $R$. Suppose that $L/K$ is a finite extension and $S$ is the in…

Let $(R,\mathfrak{m})$ be a complete discrete valuation ring with residue field $R/\mathfrak{m}=\mathbb{F}_{q}$. Let $P_{1}(t),\ldots,P_{r}(t)\in R[t]$ be monic polynomials whose r…

Let $(R,pR,k)$ be a discrete valuation ring essentially smooth over $\mathbb{Z}$, with residue field $k$. Gersten's Arithmetic DVR Conjecture. For every $n \geq 0$, the transfer ma…

Let $R$ be a DVR with residue field $k$ and let $A$ be a finite and flat $R$-algebra. Write $e^{A}$ for its ramification invariant, $\textup{rk} A$ for its rank, and…