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.
Über den Autor
Manfred Knebusch is Professor Emeritus at the University of Regensburg. He has written nine books and more than 80 papers on the algebraic theory of quadratic forms over rings and fields, valuation theory, real algebra and real algebraic geometry. His current research focusses on tropical geometry.
Claus Scheiderer is Professor at Konstanz University. His primary research interests are real algebraic geometry and convex algebraic geometry.
Thomas Unger is Associate Professor at University College Dublin. His research interests include quadratic and hermitian forms, algebras with involution, and noncommutative real algebra and geometry.
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.
