Produit tensoriel compl\'et\'e et platitude

TL;DR

This paper investigates the flatness of the completed tensor product in a more general setting than the noetherian case, providing new insights into its properties.

Contribution

It extends the understanding of flatness of completed tensor products beyond the noetherian case, addressing Shaul's question.

Findings

Provides conditions for flatness in a broader context.

Answers Shaul's question on completed tensor products.

Generalizes previous results to non-noetherian cases.

Abstract

We give, in a more general case than the noetherian case, an answer to the question posed by Shaul on the flatness of the completed tensor product.