Extension of a Weil formula in an algebraic framework
The analytic Weil formula allows to express a germ of an analytic function (at the origin) as a power series involving the elements of a regular sequence of germs and some residues. The authors present an analog of this for the algebraic case by means of the theory of algebraic residues developed by \textit{J. Lipman} in ``Residues and traces of differential forms via Hochschild homology'', Contemp. Math. 61 (1987; Zbl 0606.14015). Several examples are presented and studied. Moreover, by means of the algebraic tools developed, the authors are able to give a purely algebraic proof of the usual analytic Weil formula. If \(A\) is a noetherian ring, some criteria for the finiteness of some homomorphisms from \(A[z]\) to \(A[z]\) are also given.
noetherian ring complete with respect to the \(m\)-adic topology
scientific article; zbMATH DE number 1275773