Submersions and effective descent of étale morphisms

DOI10.24033/bsmf.2588zbMath1215.14004arXiv0710.2488OpenAlexW1506753504MaRDI QIDQ3580612

David Rydh

Publication date: 13 August 2010

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.2488

zbMATH Keywords

blow-upalgebraic spaceschemesubmersionconstructible topologyproper morphismpatch topology\(S\)-topologyeffective descentgeometric quotientétale morphism\(h\)-topology(absolute) weak normalizationfinitely presented morphismflatificationintegral morphismschematically dominant morphismsubtrusiontotally integrally closed schemeuniversally closed

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Étale and other Grothendieck topologies and (co)homologies (14F20) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Integral dependence in commutative rings; going up, going down (13B21) Étale and flat extensions; Henselization; Artin approximation (13B40) Schemes and morphisms (14A15)

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Cites Work

• Submersion et descente. (Submersion and descent)
• Quotient spaces modulo algebraic groups
• Some results on weakly normal ring extensions
• Singular homology of abstract algebraic varieties
• Homology of schemes
• Algebraic approximation of structures over complete local rings
• Totally integrally closed rings and extremal spaces
• Anneaux locaux henséliens
• Schémas en groupes. I: Propriétés générales des schémas en groupes. Exposés I à VIIb. Séminaire de Géométrie Algébrique 1962/64, dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
• Algebraic spaces
• Critères de platitude et de projectivité. Techniques de platification d'un module. (Criterial of flatness and projectivity. Technics of flatification of a module.)
• On the joints of Hensel rings
• Éléments de géométrie algébrique. I: Le langage des schémas. II: Étude globale élémentaire de quelques classe de morphismes. III: Étude cohomologique des faisceaux cohérents (première partie)
• Some properties of weakly normal varieties
• Cycles, Transfers, and Motivic Homology Theories. (AM-143)
• A new proof of D. Popescu’s theorem on smoothing of ring homomorphisms
• Lifting up an infinite chain of prime ideals to a valuation ring
• Conducteur, descente et pincement
• Autour de la platitude
• Prime Ideal Structure in Commutative Rings
• On seminormality
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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