## $\mathrm{Hom}_{A}(m/(m^2+\mu A),A/m)\cong\mathrm{Der}_\Lambda(A,A/m)$ November 28

Let $(\Lambda,\mu)$,$(A,m)$ be noetherian complete local rings, $f\colon (\Lambda,\mu)\to (A,m)$ a local homomorphism, such that $\overline{f}\colon\Lambda/\mu\to A/m$ is an isomorphism. Which one of the following is true?1) $\mathrm{Hom}_{A}(m/(m^2+