Foundations for almost ring theory -- Sixth Release

Details Foundations for almost ring theory -- Sixth Release Foundations for almost ring theory -- Sixth Release

2004-09-29

arxiv.org/abs/math/0409584v7

Mathematics

Algebraic Geometry

954 pages, written in AMS-LaTeX. Updates and corrections shall also be posted on my web page : http://math.univ-lille1.fr/~ram

Scientific paper

This is the sixth release of our project, aiming to provide a complete treatment of the foundations of almost ring theory, following and extending Faltings' method of "almost etale extensions". The central result is the "almost purity theorem". The current release is the usual mixed bag of new material and correction of old mistakes. It also includes an application to the so-called direct summand conjecture, which amplifies an idea due to B.Bhatt. The title has changed : see the revised introduction for an explanation of where the project is currently headed.

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