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Recent Progress on Submersions : A Survey and New Properties
Author
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-05-12
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
This paper is a survey about recent progress on submersive morphisms of schemes combined with new results that we prove.
They concern the class of quasicompact universally subtrusive morphisms that we introduced about 30 years ago.
They are revisited in a recent paper by Rydh, with substantial complements and key results.
We use them to show Artin-Tate-like results about the 14th problem of Hilbert, for a base scheme either Noetherian or the spectrum of a valuation domain.
We look at faithfully flat morphisms and get “almost” Artin-Tate-like results by considering the Goldman (finite type) points of a scheme.
Bjorn Poonen recently proved that universally closed morphisms are quasicompact.
By introducing incomparable morphisms of schemes, we are able to characterize universally closed surjective morphisms that are either integral or finite.
Next we consider pure morphisms of schemes introduced by Mesablishvili.
In the quasicompact case, they are universally schematically dominant morphisms.
This leads us to a characterization of universally subtrusive morphisms by purity.
Some results on the schematically dominant property are given.
The paper ends with properties of monomorphisms and topological immersions, a dual notion of submersions.
American Psychological Association (APA)
Picavet, Gabriel. 2013. Recent Progress on Submersions : A Survey and New Properties. Algebra،Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-447858
Modern Language Association (MLA)
Picavet, Gabriel. Recent Progress on Submersions : A Survey and New Properties. Algebra No. 2013 (2013), pp.1-14.
https://search.emarefa.net/detail/BIM-447858
American Medical Association (AMA)
Picavet, Gabriel. Recent Progress on Submersions : A Survey and New Properties. Algebra. 2013. Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-447858
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-447858