Sul rango del modulo finito dei differenziali in caratteristica diseguale

Imbesi, Maurizio (1990) Sul rango del modulo finito dei differenziali in caratteristica diseguale. Accademia Peloritana dei Pericolanti Classe FF.MM.NN., 68. pp. 243-255.

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We find a superior bound for the rank $\mu(D_A_/_I)$ of the finite differential module $D_A_/_I$ of a local ring $(A, m)$ whose characteristic is equal to zero and which contains a $DVR I$ with parameter the prime number $p > O$; exactly if we suppose that $p \not\in m^2$, $A/m$ is separably generated over $I/pI$ and $\rho$ = tr. deg $(A/m : I/pI) < \infty$ , prove that $\mu(D_A_/_I) \le \ Dim(A)-1 + \rho$, where $Dim(A)$ is the embedding dimension of $A$. Indeed, if $p \in m^2$, we obtain the superior bound $\mu(D_A_/_I) \le \ Dim(A) + \rho$, under some restrictive conditions over $A$.