Real and Etale Cohomology

Claus Scheiderer (Autor)

Buch | Softcover

XXIV, 284 Seiten

1994 | 1994
Springer Berlin (Verlag)
978-3-540-58436-0 (ISBN)

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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.

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.

Erscheint lt. Verlag	27.10.1994
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XXIV, 284 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	468 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebraic Geometry • cohomology • Cohomology theory • Dimension • Grad • Grothendieck Topology • Homology • topological group • Zariski topology
ISBN-10	3-540-58436-6 / 3540584366
ISBN-13	978-3-540-58436-0 / 9783540584360
Zustand	Neuware