arXiv subjects
Publications and source records attributed to M. Fernandez-Lebron.
Let k be a perfect field of positive characteristic, k(t)_{per} the perfect closure of k(t) and A=k[[X_1,...,X_n]]. We show that for any maximal ideal N of A'=k(t)_{per}\otimes_k A, the elements in \hat{A'_N} which are annihilated by the "Taylor" Hasse-Schmidt derivations with respect to the X_i form a coefficient field of \hat{A'_N}.
We show how to express any Hasse-Schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis. As an application, we obtain coefficient fields of the completion of a regular local ring of positive characteristic in terms of Hasse-Schmidt derivations
Let $k$ be a perfect field of characteristic $p>0$, $k(t)_{per}$ the perfect closure of $k(t)$ and $A$ a $k$-algebra. We characterize whether the ring $A\otimes_k k(t)_{per}$ is noetherian or not. As a consequence, we prove that the ring $A\otimes_k k(t)_{per}$ is noetherian when $A$ is the ring of formal power series in $n$ indeterminates over $k$.