Loading...
Please wait, while we are loading the content...
Similar Documents
Almost Ring Theory
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2000 |
| Abstract | Broadly speaking, the aim of this work is to describe “how to d o ring theory” within monoidal categories that arise as localisations of categories of mod ules over certain rings. A reader looking for forerunners of our themes would be drawn inevitably t o Gabriel’s “Des categories abeliennes” [8], and might even conclude that Gabriel’s memoir mu st have been the main instigation for the present article. In truth, the initial motivation is to be found elsewhere, namely in the want of adequately documented foundations for the method of almost étale extensions that underpins Faltings’ approach to p-adic Hodge theory as presented in [6]. However, as is often t h case with healthy offsprings, our subject matter has eventu ally resolved to venture beyond its original boundaries and pursue an autonomous existence. In any case, we are glad to report that our paper remains true t o its first vocation, which is to serve as a comprehensive reference, paving the way to deep er as ects of almost étale theory, especially to the difficult purity theorem of [6]. The notion s of almost unramified and almost étale morphism are defined and their main properties are est ablished, including the analogues of the classical lifting theorems over nilpotent extensions, and invariance under Frobenius. Also, to any almost finitely presented almost flat morphism we attac h an almost trace form, and we characterize almost étale morphisms in terms of this form. Finally, we study some cases of non-flat descent for almost étale maps. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0201175v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0002064v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0201175v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0201175v3.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Autonomous robot Categories Diethylstilbestrol Document completion status - Documented Foundations Lifting scheme Map Matrix multiplication Pure function Ring device Speaking (activity) Subject matter expert Turing test |
| Content Type | Text |
| Resource Type | Article |
