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Beschreibung
This book makes a systematic study of the relations between the étale cohomology of a scheme and the orderings of its residue fields. A major result is that in high degrees, étale cohomology is cohomology of the real spectrum. It also contains new contributions in group cohomology and in topos theory. It is of interest to graduate students and researchers who work in algebraic geometry (not only real) and have some familiarity with the basics of étale cohomology and Grothendieck sites. Independently, it is of interest to people working in the cohomology theory of groups or in topos theory.
This book makes a systematic study of the relations between the étale cohomology of a scheme and the orderings of its residue fields. A major result is that in high degrees, étale cohomology is cohomology of the real spectrum. It also contains new contributions in group cohomology and in topos theory. It is of interest to graduate students and researchers who work in algebraic geometry (not only real) and have some familiarity with the basics of étale cohomology and Grothendieck sites. Independently, it is of interest to people working in the cohomology theory of groups or in topos theory.
Inhaltsverzeichnis
Real spectrum and real étale site.- Glueing étale and real étale site.- Limit theorems, stalks, and other basic facts.- Some reminders on Weil restrictions.- Real spectrum of X and étale site of .- The fundamental long exact sequence.- Cohomological dimension of X b , I: Reduction to the field case.- Equivariant sheaves for actions of topological groups.- Cohomological dimension of X b , II: The field case.- G-toposes.- Inverse limits of G-toposes: Two examples.- Group actions on spaces: Topological versus topos-theoretic constructions.- Quotient topos of a G-topos, for G of prime order.- Comparison theorems.- Base change theorems.- Constructible sheaves and finiteness theorems.- Cohomology of affine varieties.- Relations to the Zariski topology.- Examples and complements.
Details
Erscheinungsjahr: 1994
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Lecture Notes in Mathematics
Inhalt: Einband - flex.(Paperback)
ISBN-13: 9783540584360
ISBN-10: 3540584366
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Scheiderer, Claus
Hersteller: Springer
Springer Vieweg
Springer-Verlag GmbH
Lecture Notes in Mathematics
Verantwortliche Person für die EU: Springer Nature Customer Service Center GmbH, Europaplatz 3, D-69115 Heidelberg, productsafety@springernature.com
Maße: 235 x 155 x 17 mm
Von/Mit: Claus Scheiderer
Erscheinungsdatum: 27.10.1994
Gewicht: 0,47 kg
Artikel-ID: 101894972